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Ashfaque (MInstP)</a><p class="suggested-user-card__user-info__subheader ds2-5-body-xs">Independent Researcher</p></div></div><div class="suggested-user-card"><div class="suggested-user-card__avatar social-profile-avatar-container"><a href="https://nmsu.academia.edu/ANNIESELDEN"><img class="profile-avatar u-positionAbsolute" alt="ANNIE SELDEN" border="0" onerror="if (this.src != '//a.academia-assets.com/images/s200_no_pic.png') this.src = '//a.academia-assets.com/images/s200_no_pic.png';" width="200" height="200" src="https://0.academia-photos.com/2931250/968891/3597910/s200_annie.selden.jpg" /></a></div><div class="suggested-user-card__user-info"><a class="suggested-user-card__user-info__header ds2-5-body-sm-bold ds2-5-body-link" href="https://nmsu.academia.edu/ANNIESELDEN">ANNIE SELDEN</a><p class="suggested-user-card__user-info__subheader ds2-5-body-xs">New Mexico State University</p></div></div><div class="suggested-user-card"><div class="suggested-user-card__avatar 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href="https://uken.academia.edu/TomaszSzemberg">Tomasz Szemberg</a><p class="suggested-user-card__user-info__subheader ds2-5-body-xs">University of the National Education Commission in Krakow</p></div></div><div class="suggested-user-card"><div class="suggested-user-card__avatar social-profile-avatar-container"><a href="https://syr.academia.edu/JackGraver"><img class="profile-avatar u-positionAbsolute" alt="Jack Graver" border="0" onerror="if (this.src != '//a.academia-assets.com/images/s200_no_pic.png') this.src = '//a.academia-assets.com/images/s200_no_pic.png';" width="200" height="200" src="https://0.academia-photos.com/32585458/36635056/31298675/s200_jack.graver.png" /></a></div><div class="suggested-user-card__user-info"><a class="suggested-user-card__user-info__header ds2-5-body-sm-bold ds2-5-body-link" href="https://syr.academia.edu/JackGraver">Jack Graver</a><p class="suggested-user-card__user-info__subheader ds2-5-body-xs">Syracuse University</p></div></div><div class="suggested-user-card"><div class="suggested-user-card__avatar social-profile-avatar-container"><a href="https://uj-pl.academia.edu/JerzyWeyman"><img class="profile-avatar u-positionAbsolute" border="0" alt="" src="//a.academia-assets.com/images/s200_no_pic.png" /></a></div><div class="suggested-user-card__user-info"><a class="suggested-user-card__user-info__header ds2-5-body-sm-bold ds2-5-body-link" href="https://uj-pl.academia.edu/JerzyWeyman">Jerzy Weyman</a><p class="suggested-user-card__user-info__subheader ds2-5-body-xs">Jagiellonian University in Krakow</p></div></div><div class="suggested-user-card"><div class="suggested-user-card__avatar social-profile-avatar-container"><a href="https://uel.academia.edu/JanaJavornik"><img class="profile-avatar u-positionAbsolute" alt="Jana Javornik" border="0" onerror="if (this.src != '//a.academia-assets.com/images/s200_no_pic.png') this.src = '//a.academia-assets.com/images/s200_no_pic.png';" width="200" height="200" src="https://0.academia-photos.com/113072/30527/13170018/s200_jana.javornik.jpg" /></a></div><div class="suggested-user-card__user-info"><a class="suggested-user-card__user-info__header ds2-5-body-sm-bold ds2-5-body-link" href="https://uel.academia.edu/JanaJavornik">Jana Javornik</a><p class="suggested-user-card__user-info__subheader ds2-5-body-xs">University of East London</p></div></div><div class="suggested-user-card"><div class="suggested-user-card__avatar social-profile-avatar-container"><a href="https://uncg.academia.edu/GwenRobbinsSchug"><img class="profile-avatar u-positionAbsolute" alt="Gwen Robbins Schug" border="0" onerror="if (this.src != '//a.academia-assets.com/images/s200_no_pic.png') this.src = '//a.academia-assets.com/images/s200_no_pic.png';" width="200" height="200" src="https://0.academia-photos.com/161482/41323/141954071/s200_gwen.robbins_schug.jpg" /></a></div><div class="suggested-user-card__user-info"><a class="suggested-user-card__user-info__header ds2-5-body-sm-bold ds2-5-body-link" href="https://uncg.academia.edu/GwenRobbinsSchug">Gwen Robbins Schug</a><p class="suggested-user-card__user-info__subheader ds2-5-body-xs">University of North Carolina at Greensboro</p></div></div></ul></div><div class="ri-section"><div class="ri-section-header"><span>Interests</span></div><div class="ri-tags-container"><a data-click-track="profile-user-info-expand-research-interests" data-has-card-for-ri-list="194013305" href="https://www.academia.edu/Documents/in/Pure_Mathematics"><div id="js-react-on-rails-context" style="display:none" data-rails-context="{"inMailer":false,"i18nLocale":"en","i18nDefaultLocale":"en","href":"https://independent.academia.edu/AmirMafi2","location":"/AmirMafi2","scheme":"https","host":"independent.academia.edu","port":null,"pathname":"/AmirMafi2","search":null,"httpAcceptLanguage":null,"serverSide":false}"></div> <div class="js-react-on-rails-component" style="display:none" data-component-name="Pill" data-props="{"color":"gray","children":["Pure Mathematics"]}" data-trace="false" data-dom-id="Pill-react-component-f0d8bfb7-895f-4cd4-812a-236af2c41fff"></div> <div id="Pill-react-component-f0d8bfb7-895f-4cd4-812a-236af2c41fff"></div> </a><a data-click-track="profile-user-info-expand-research-interests" data-has-card-for-ri-list="194013305" href="https://www.academia.edu/Documents/in/Blow_Up"><div class="js-react-on-rails-component" style="display:none" data-component-name="Pill" data-props="{"color":"gray","children":["Blow Up"]}" data-trace="false" data-dom-id="Pill-react-component-aa592132-0a79-4e91-810e-b4a92fd43363"></div> <div id="Pill-react-component-aa592132-0a79-4e91-810e-b4a92fd43363"></div> </a><a data-click-track="profile-user-info-expand-research-interests" data-has-card-for-ri-list="194013305" href="https://www.academia.edu/Documents/in/Mathematics"><div class="js-react-on-rails-component" style="display:none" data-component-name="Pill" data-props="{"color":"gray","children":["Mathematics"]}" data-trace="false" data-dom-id="Pill-react-component-cc2a1702-165a-4154-95e4-d9a204c0531c"></div> <div id="Pill-react-component-cc2a1702-165a-4154-95e4-d9a204c0531c"></div> </a></div></div></div></div><div class="right-panel-container"><div class="user-content-wrapper"><div class="uploads-container" id="social-redesign-work-container"><div class="upload-header"><h2 class="ds2-5-heading-sans-serif-xs">Uploads</h2></div><div class="documents-container backbone-social-profile-documents" style="width: 100%;"><div class="u-taCenter"></div><div class="profile--tab_content_container js-tab-pane tab-pane active" id="all"><div class="profile--tab_heading_container js-section-heading" data-section="Papers" id="Papers"><h3 class="profile--tab_heading_container">Papers by Amir Mafi</h3></div><div class="js-work-strip profile--work_container" data-work-id="83227340"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" rel="nofollow" href="https://www.academia.edu/83227340/Some_criteria_for_the_Cohen_Macaulay_property_and_local_cohomology"><img alt="Research paper thumbnail of Some criteria for the Cohen-Macaulay property and local cohomology" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" rel="nofollow" href="https://www.academia.edu/83227340/Some_criteria_for_the_Cohen_Macaulay_property_and_local_cohomology">Some criteria for the Cohen-Macaulay property and local cohomology</a></div><div class="wp-workCard_item"><span>Acta Mathematica Sinica, English Series</span><span>, 2009</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">ABSTRACT Let a be an ideal of a commutative Noetherian ring R and M be a finitely generated R-mod...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">ABSTRACT Let a be an ideal of a commutative Noetherian ring R and M be a finitely generated R-module of dimension d. We characterize Cohen-Macaulay rings in term of a special homological dimension. Lastly, we prove that if R is a complete local ring, then the Matlis dual of top local cohomology module H a d (M) is a Cohen-Macaulay R-module provided that the R-module M satisfies some conditions.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="83227340"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="83227340"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 83227340; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=83227340]").text(description); $(".js-view-count[data-work-id=83227340]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 83227340; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='83227340']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=83227340]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":83227340,"title":"Some criteria for the Cohen-Macaulay property and local cohomology","internal_url":"https://www.academia.edu/83227340/Some_criteria_for_the_Cohen_Macaulay_property_and_local_cohomology","owner_id":194013305,"coauthors_can_edit":true,"owner":{"id":194013305,"first_name":"Amir","middle_initials":null,"last_name":"Mafi","page_name":"AmirMafi2","domain_name":"independent","created_at":"2021-05-22T06:14:23.216-07:00","display_name":"Amir Mafi","url":"https://independent.academia.edu/AmirMafi2"},"attachments":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="71947427"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/71947427/Results_on_Almost_Cohen_Macaulay_Modules"><img alt="Research paper thumbnail of Results on Almost Cohen-Macaulay Modules" class="work-thumbnail" src="https://attachments.academia-assets.com/81081301/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/71947427/Results_on_Almost_Cohen_Macaulay_Modules">Results on Almost Cohen-Macaulay Modules</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Let (R, m) be a commutative Noetherian local ring, and M be a non-zero finitely-generated R-modul...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Let (R, m) be a commutative Noetherian local ring, and M be a non-zero finitely-generated R-module. We show that if R is almost Cohen-Macaulay and M is perfect with finite projective dimension, then M is an almost Cohen-Macaulay module. Also, we give some necessary and sufficient conditions on M to be an almost Cohen-Macaulay module, by using Ext functors.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="41d67b39a9b6a2332833f586b35ec589" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":81081301,"asset_id":71947427,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/81081301/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="71947427"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="71947427"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 71947427; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="71947419"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" rel="nofollow" href="https://www.academia.edu/71947419/A_New_Characterization_of_Commutative_Artinian_Rings"><img alt="Research paper thumbnail of A New Characterization of Commutative Artinian Rings" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" rel="nofollow" href="https://www.academia.edu/71947419/A_New_Characterization_of_Commutative_Artinian_Rings">A New Characterization of Commutative Artinian Rings</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Abstract. Let R be a commutative Noetherian ring. It is shown that R is Artinian if and only if e...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Abstract. Let R be a commutative Noetherian ring. It is shown that R is Artinian if and only if every R-module is good, if and only if every R-module is representable. As a result, it follows that every nonzero submodule of any representable R-module is representable if and only if R is Artinian. This provides an answer to a question which is investigated in [1]. 1.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="71947419"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="71947419"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 71947419; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=71947419]").text(description); $(".js-view-count[data-work-id=71947419]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 71947419; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='71947419']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=71947419]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":71947419,"title":"A New Characterization of Commutative Artinian Rings","internal_url":"https://www.academia.edu/71947419/A_New_Characterization_of_Commutative_Artinian_Rings","owner_id":194013305,"coauthors_can_edit":true,"owner":{"id":194013305,"first_name":"Amir","middle_initials":null,"last_name":"Mafi","page_name":"AmirMafi2","domain_name":"independent","created_at":"2021-05-22T06:14:23.216-07:00","display_name":"Amir Mafi","url":"https://independent.academia.edu/AmirMafi2"},"attachments":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="71947360"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/71947360/Sequentially_Cohen_Macaulay_matroidal_ideals"><img alt="Research paper thumbnail of Sequentially Cohen-Macaulay matroidal ideals" class="work-thumbnail" src="https://attachments.academia-assets.com/81081254/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/71947360/Sequentially_Cohen_Macaulay_matroidal_ideals">Sequentially Cohen-Macaulay matroidal ideals</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Let R=K[x_1,...,x_n] be the polynomial ring in n variables over a field K and let J be a matroida...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Let R=K[x_1,...,x_n] be the polynomial ring in n variables over a field K and let J be a matroidal ideal of degree d in R. In this paper, we study the class of sequentially Cohen-Macaulay matroidal ideals. In particular, all sequentially Cohen-Macaulay matroidal ideals of degree 2 are classified. Furthermore, we give a classification of sequentially Cohen-Macaulay matroidal ideals of degree d≥ 3 in some special cases.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="ba9614012e3b5fd83bc3076e444de1cf" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":81081254,"asset_id":71947360,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/81081254/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="71947360"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="71947360"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 71947360; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="66935677"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/66935677/Sequentially_cohen_macaulay_matroidal_ideals"><img alt="Research paper thumbnail of Sequentially cohen-macaulay matroidal ideals" class="work-thumbnail" src="https://attachments.academia-assets.com/77943114/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/66935677/Sequentially_cohen_macaulay_matroidal_ideals">Sequentially cohen-macaulay matroidal ideals</a></div><div class="wp-workCard_item"><span>Filomat</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Let R = K[x1,...,xn] be the polynomial ring in n variables over a field K and let I be a matroida...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Let R = K[x1,...,xn] be the polynomial ring in n variables over a field K and let I be a matroidal ideal of degree d in R. Our main focus is determining when matroidal ideals are sequentially Cohen- Macaulay. In particular, all sequentially Cohen-Macaulay matroidal ideals of degree 2 are classified. Furthermore, we give a classification of sequentially Cohen-Macaulay matroidal ideals of degree d ? 3 in some special cases.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="5700a99e1063e4be292e5406998df89e" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":77943114,"asset_id":66935677,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/77943114/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="66935677"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="66935677"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 66935677; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="66935676"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/66935676/The_saturation_number_of_powers_of_graded_ideals"><img alt="Research paper thumbnail of The saturation number of powers of graded ideals" class="work-thumbnail" src="https://attachments.academia-assets.com/77943041/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/66935676/The_saturation_number_of_powers_of_graded_ideals">The saturation number of powers of graded ideals</a></div><div class="wp-workCard_item"><span>arXiv: Commutative Algebra</span><span>, 2019</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Let $S=K[x_1,\ldots,x_n]$ be the polynomial ring in $n$ variables over a field $K$ with maximal i...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Let $S=K[x_1,\ldots,x_n]$ be the polynomial ring in $n$ variables over a field $K$ with maximal ideal $\frak{m}=(x_1,...,x_n)$, and let $I$ be a graded ideal of $S$. In this paper, we define the saturation number $\sat(I)$ of $I$ to be the smallest non-negative integer $k$ such that $I:\mm^{k+1}= I:\mm^k$. We show that $f(k)$ is linearly bounded, and that $f(k)$ is a quasi-linear function for $k\gg 0$, if $I$ is a monomial ideal. Furthermore, we show that $\sat(I^k)=k$ if $I$ is a principal Borel ideal and prove that $\sat(I_{d,n}^k) =\max\{l\:\; (kd-l)/(k-l) \leq n\},$ where $I_{d,n}$ is the squarefree Veronese ideal generated in degree $d$. \end{abstract}</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="26509d11f7faa0878b8c8cac70752269" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":77943041,"asset_id":66935676,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/77943041/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="66935676"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="66935676"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 66935676; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="66935675"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/66935675/On_the_first_generalized_Hilbert_coefficient_and_depth_of_associated_graded_rings"><img alt="Research paper thumbnail of On the first generalized Hilbert coefficient and depth of associated graded rings" class="work-thumbnail" src="https://attachments.academia-assets.com/77943038/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/66935675/On_the_first_generalized_Hilbert_coefficient_and_depth_of_associated_graded_rings">On the first generalized Hilbert coefficient and depth of associated graded rings</a></div><div class="wp-workCard_item"><span>arXiv: Commutative Algebra</span><span>, 2017</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Let $(R,\mathfrak{m})$ be a $d$-dimensional Cohen-Macaulay local ring with infinite residue field...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Let $(R,\mathfrak{m})$ be a $d$-dimensional Cohen-Macaulay local ring with infinite residue field. Let $I$ be an ideal of $R$ that has analytic spread $\ell(I)=d$, satisfies the $G_d$ condition, the weak Artin-Nagata property $AN_{d-2}^-$ and depth$(R/I)\geq\min\lbrace 1,\dim R/I \rbrace$. In this paper, we show that if $j_1(I) = \lambda (I/J) +\lambda [R/(J_{d-1} :_{R} I+(J_{d-2} :_{R}I+I) :_R, \mathfrak{m}^\infty)]+1$, then depth$(G(I))\geq d -1$ and $r_J(I)\leq 2$, where $J$ is a general minimal reduction of $I$. In addition, we extend the result by Sally who has studied the depth of associated graded rings and minimal reductions for an $,\mathfrak{m}$-primary ideals.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="ebd24b6b8e24b1fa873e8adf5db6c794" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":77943038,"asset_id":66935675,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/77943038/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="66935675"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="66935675"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 66935675; 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For a non-ne...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Let a ⊆ b be two ideals of commutative Noetherian ring R and A an Artinian R-module. For a non-negative integer n, we show that up+q=n Ann(Torp (R/b, H q (A))) ⊆ Ann(Torn (R/b, A)). As an immediate consequence, if H i (A) is Artinian for all i &lt; n then a ⊆ Rad(Ann(H i (A))) for all i &lt; n. 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Thus, in that case one can compute the depth of associated graded ring of as In this paper we extend results in case of rings and ideals to the case of modules and we show that for associated graded module of with respect to i.e, , such an equality is also valid when is not necessarily Cohen-Macaulay, and we extend Burch’s inequality to modules. Also, we compute the Rees Algebra and associated graded ring of generically complete intersection of an ideal with respect to module in local Cohen - Macaulay ring and we obtain positive results for ideals with analytic deviation less or equal than one and reduction number at most two with respect to module</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="66935673"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="66935673"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 66935673; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=66935673]").text(description); $(".js-view-count[data-work-id=66935673]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 66935673; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='66935673']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=66935673]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":66935673,"title":"Results on Generalization of Burch’s Inequality and the Depth of Rees Algebra and Associated Graded Rings of an Ideal with Respect to a Cohen-Macaulay Module","internal_url":"https://www.academia.edu/66935673/Results_on_Generalization_of_Burch_s_Inequality_and_the_Depth_of_Rees_Algebra_and_Associated_Graded_Rings_of_an_Ideal_with_Respect_to_a_Cohen_Macaulay_Module","owner_id":194013305,"coauthors_can_edit":true,"owner":{"id":194013305,"first_name":"Amir","middle_initials":null,"last_name":"Mafi","page_name":"AmirMafi2","domain_name":"independent","created_at":"2021-05-22T06:14:23.216-07:00","display_name":"Amir Mafi","url":"https://independent.academia.edu/AmirMafi2"},"attachments":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="66935670"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/66935670/Almost_Cohen_Macaulayness_of_Koszul_Homology"><img alt="Research paper thumbnail of Almost Cohen-Macaulayness of Koszul Homology" class="work-thumbnail" src="https://attachments.academia-assets.com/77943035/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/66935670/Almost_Cohen_Macaulayness_of_Koszul_Homology">Almost Cohen-Macaulayness of Koszul Homology</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Let (R,m) be a commutative Noetherian ring, I an ideal of R and M a non-zero finitely generated R...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Let (R,m) be a commutative Noetherian ring, I an ideal of R and M a non-zero finitely generated R-module. We show that if M and H0(I,M) are aCM R-modules and I = (x1, . . . , xn+1) such that x1, . . . , xn is an M -regular sequence, then Hi(I,M) is an aCM R-module for all i. Moreover, we prove that if R and Hi(I, R) are aCM for all i, then R/(0 : I) is aCM. In addition, we prove that if R is aCM and x1, . . . , xn is an aCM d-sequence, then depthHi(x1, . . . , xn;R) ≥ i− 1 for all i.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="6146a1c5837d9bfff1b43036610445ff" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":77943035,"asset_id":66935670,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/77943035/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="66935670"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="66935670"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 66935670; 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Если $M$ - максимальный $R$-модуль Коэна-Маколея, то для достаточно больших $n$ и $1\le i\le d$ длины модулей $\operatorname{Ext}^i_R(R/J,M/I^nM)$ и $\operatorname{Tor}_i^R(R/J,M/I^nM)$ - полиномы степени $d-1$. Кроме того, показано, что $$ \operatorname{deg}\beta_i^R(M/I^nM) =\operatorname{deg}\mu^i_R(M/I^nM)=d-1, $$ где $\beta_i^R( \cdot )$ и $\mu^i_R( \cdot )$ - $i$-е число Бетти и $i$-е число Басса, соответственно. Библиография: 14 названий.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="66935668"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="66935668"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 66935668; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=66935668]").text(description); $(".js-view-count[data-work-id=66935668]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 66935668; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='66935668']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=66935668]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":66935668,"title":"О степени гильбертовых полиномов производных функторов","internal_url":"https://www.academia.edu/66935668/%D0%9E_%D1%81%D1%82%D0%B5%D0%BF%D0%B5%D0%BD%D0%B8_%D0%B3%D0%B8%D0%BB%D1%8C%D0%B1%D0%B5%D1%80%D1%82%D0%BE%D0%B2%D1%8B%D1%85_%D0%BF%D0%BE%D0%BB%D0%B8%D0%BD%D0%BE%D0%BC%D0%BE%D0%B2_%D0%BF%D1%80%D0%BE%D0%B8%D0%B7%D0%B2%D0%BE%D0%B4%D0%BD%D1%8B%D1%85_%D1%84%D1%83%D0%BD%D0%BA%D1%82%D0%BE%D1%80%D0%BE%D0%B2","owner_id":194013305,"coauthors_can_edit":true,"owner":{"id":194013305,"first_name":"Amir","middle_initials":null,"last_name":"Mafi","page_name":"AmirMafi2","domain_name":"independent","created_at":"2021-05-22T06:14:23.216-07:00","display_name":"Amir Mafi","url":"https://independent.academia.edu/AmirMafi2"},"attachments":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="66935667"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" rel="nofollow" href="https://www.academia.edu/66935667/Gorenstein_homological_dimension_and_Ext_depth_of_modules"><img alt="Research paper thumbnail of Gorenstein homological dimension and Ext-depth of modules" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" rel="nofollow" href="https://www.academia.edu/66935667/Gorenstein_homological_dimension_and_Ext_depth_of_modules">Gorenstein homological dimension and Ext-depth of modules</a></div><div class="wp-workCard_item"><span>Bulletin of the Belgian Mathematical Society - Simon Stevin</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">ABSTRACT Let $(R,{\frak{m}},k)$ be a commutative Noetherian local ring. It is well-known that $R$...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">ABSTRACT Let $(R,{\frak{m}},k)$ be a commutative Noetherian local ring. It is well-known that $R$ is regular if and only if the flat dimension of $k$ is finite. In this paper, we show that $R$ is Gorenstein if and only if the Gorenstein flat dimension of $k$ is finite. Also, we will show that if $R$ is a Cohen-Macaulay ring and $M$ is a Tor-finite $R$-module of finite Gorenstein flat dimension, then the depth of the ring is equal to the sum of the Gorenstein flat dimension and Ext-depth of $M$. As a consequence, we get that this formula holds for every syzygy of a finitely generated $R$-module over a Gorenstein local ring.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="66935667"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="66935667"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 66935667; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=66935667]").text(description); $(".js-view-count[data-work-id=66935667]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 66935667; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='66935667']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=66935667]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":66935667,"title":"Gorenstein homological dimension and Ext-depth of modules","internal_url":"https://www.academia.edu/66935667/Gorenstein_homological_dimension_and_Ext_depth_of_modules","owner_id":194013305,"coauthors_can_edit":true,"owner":{"id":194013305,"first_name":"Amir","middle_initials":null,"last_name":"Mafi","page_name":"AmirMafi2","domain_name":"independent","created_at":"2021-05-22T06:14:23.216-07:00","display_name":"Amir Mafi","url":"https://independent.academia.edu/AmirMafi2"},"attachments":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="66935665"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/66935665/On_stability_properties_of_powers_of_polymatroidal_ideals"><img alt="Research paper thumbnail of On stability properties of powers of polymatroidal ideals" class="work-thumbnail" src="https://attachments.academia-assets.com/77943116/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/66935665/On_stability_properties_of_powers_of_polymatroidal_ideals">On stability properties of powers of polymatroidal ideals</a></div><div class="wp-workCard_item"><span>Collectanea Mathematica</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Let R = K[x 1 , ..., x n ] be the polynomial ring in n variables over a field K with the maximal ...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Let R = K[x 1 , ..., x n ] be the polynomial ring in n variables over a field K with the maximal ideal m = (x 1 , ..., x n). Let astab(I) and dstab(I) be the smallest integer n for which Ass(I n) and depth(I n) stabilize, respectively. In this paper we show that astab(I) = dstab(I) in the following cases: (i) I is a matroidal ideal and n ≤ 5. (ii) I is a polymatroidal ideal, n = 4 and m / ∈ Ass ∞ (I), where Ass ∞ (I) is the stable set of associated prime ideals of I. (iii) I is a polymatroidal ideal of degree 2. Moreover, we give an example of a polymatroidal ideal for which astab(I) = dstab(I). This is a counterexample to the conjecture of Herzog and Qureshi, according to which these two numbers are the same for polymatroidal ideals.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="9f919f7c28489fceac8d91e0129c1ac1" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":77943116,"asset_id":66935665,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/77943116/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="66935665"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="66935665"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 66935665; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=66935665]").text(description); $(".js-view-count[data-work-id=66935665]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 66935665; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='66935665']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "9f919f7c28489fceac8d91e0129c1ac1" } } $('.js-work-strip[data-work-id=66935665]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":66935665,"title":"On stability properties of powers of polymatroidal ideals","internal_url":"https://www.academia.edu/66935665/On_stability_properties_of_powers_of_polymatroidal_ideals","owner_id":194013305,"coauthors_can_edit":true,"owner":{"id":194013305,"first_name":"Amir","middle_initials":null,"last_name":"Mafi","page_name":"AmirMafi2","domain_name":"independent","created_at":"2021-05-22T06:14:23.216-07:00","display_name":"Amir Mafi","url":"https://independent.academia.edu/AmirMafi2"},"attachments":[{"id":77943116,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/77943116/thumbnails/1.jpg","file_name":"1803.00730v2.pdf","download_url":"https://www.academia.edu/attachments/77943116/download_file","bulk_download_file_name":"On_stability_properties_of_powers_of_pol.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/77943116/1803.00730v2-libre.pdf?1641215122=\u0026response-content-disposition=attachment%3B+filename%3DOn_stability_properties_of_powers_of_pol.pdf\u0026Expires=1739845661\u0026Signature=b752k3P~vrW~iPAEXkc7SRDWl1dCIBGN04FSXxXpsDBJu8nfkxaEILVFGq4S1JhS5YtFE2-fmYzUOjaWGpIq4i2gPVv2sENCP8aMZlrllVY~i~xxfHCWfATLoCUQaUvkR2hqR3PcfswlZvJvKLPZB1uPFvFwktfBY-i9KRdvoB~L3EWSTd4~nqi9bFOtcoIOLfzqDQePX0qgqgd4NRJ4kIRUqO763BiA2maLY2pkQY~0-Ew2sDeKLH6IXmGL2w1HmmpLBPz6i~0G8qwiZ3d7CQOjFuRjgNazHws9updysiu82IFrNCR3tabdSnpK6Exbb8jaEUfpg6V4Ucz77bHQXg__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="66935664"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/66935664/Effect_of_Perioperative_Management_on_Outcome_of_Patients_after_Craniosynostosis_Surgery"><img alt="Research paper thumbnail of Effect of Perioperative Management on Outcome of Patients after Craniosynostosis Surgery" class="work-thumbnail" src="https://attachments.academia-assets.com/77943111/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/66935664/Effect_of_Perioperative_Management_on_Outcome_of_Patients_after_Craniosynostosis_Surgery">Effect of Perioperative Management on Outcome of Patients after Craniosynostosis Surgery</a></div><div class="wp-workCard_item"><span>World journal of plastic surgery</span><span>, 2017</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Craniosynostosis results from premature closure of one or more cranial sutures, leading to deform...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Craniosynostosis results from premature closure of one or more cranial sutures, leading to deformed calvaria and craniofacial skeleton at birth. Postoperative complications and outcome in intensive care unit (ICU) is related to surgical method and perioperative management. This study determined the perioperative risk factors, which affect outcome of patients after craniosynostosis surgery. In a retrospective study, 178 patients with craniosynostosis who underwent primary cranial reconstruction were included. Postoperative complications following neurosurgical procedures including fever in ICU, level of consciousness, re-intubation, and blood, urine, and other cultures were also performed and their association with the main outcomes (length of ICU stay) were analyzed. Factors independently associated with a longer pediatric ICU stay were fever (OR=1.59, 95% CI=1.25-4.32; p=0.001), perioperative bleeding (OR=2.25, 95% CI=1.65-3.65; p=0.01), age (having surgery after the first 5 years)...</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="1f86a304985580dcad8105fb8aa0ccdf" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":77943111,"asset_id":66935664,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/77943111/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="66935664"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="66935664"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 66935664; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=66935664]").text(description); $(".js-view-count[data-work-id=66935664]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 66935664; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='66935664']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="66935663"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/66935663/On_the_finiteness_of_local_homology_modules"><img alt="Research paper thumbnail of On the finiteness of local homology modules" class="work-thumbnail" src="https://attachments.academia-assets.com/77943110/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/66935663/On_the_finiteness_of_local_homology_modules">On the finiteness of local homology modules</a></div><div class="wp-workCard_item"><span>Rendiconti Del Seminario Matematico</span><span>, 2009</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Let (R,m) be a commutative Noetherian complete local ring, a an ideal of R, and A an Artinian R-m...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Let (R,m) be a commutative Noetherian complete local ring, a an ideal of R, and A an Artinian R-module with N-dim A = d. We prove that if d > 0, then Cosupp(H a d−1 (A)) is finite and if d ≤ 3, then the set Coass(H a i (A)) is finite for all i. Moreover, if either d ≤ 2 or the cohomological dimension cd(a) = 1 then H a i (A) is a-coartinian for all i; that is, Tor R j (R/a,H a i (A)) is Artinian for all i, j. We also show that if H a i (A) is a-coartinian for all i < n, then Tor R j (R/a,H a n (A)) is Artinian for j = 0,1. In particular, the set Coass(H a n (A)) is finite.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="1054e32c642c50cb2477f6235a55869d" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":77943110,"asset_id":66935663,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/77943110/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="66935663"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="66935663"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 66935663; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="66935662"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/66935662/Top_generalized_local_cohomology_modules"><img alt="Research paper thumbnail of Top generalized local cohomology modules" class="work-thumbnail" src="https://attachments.academia-assets.com/77943031/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/66935662/Top_generalized_local_cohomology_modules">Top generalized local cohomology modules</a></div><div class="wp-workCard_item"><span>Turkish Journal of Mathematics</span><span>, 2011</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Let (R, Ñ) be a commutative Noetherian local ring and M , N two non-zero finitely generated Rmodu...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Let (R, Ñ) be a commutative Noetherian local ring and M , N two non-zero finitely generated Rmodules with pd(M) = n < ∞ and dim(N) = d. In this paper, we show that if the top generalized local cohomology module H n+d Ñ (M, N) = 0 , then the following statements are equivalent: (i) Ann(0 : H d m (N) Ô) = Ô for all Ô ∈ Var(Ann(H d Ñ (N))) ; (ii) Ann(0 : H n+d m (M,N) Ô) = Ô for all Ô ∈ Var(Ann(H n+d Ñ (M, N))) .</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="b091e5c3c597a022761855cad765d979" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":77943031,"asset_id":66935662,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/77943031/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="66935662"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="66935662"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 66935662; 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Some basic properties an...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">In this paper we study the class of sequentially Cohen-Macaulay modules. Some basic properties and characterizations of these modules in terms of Ext-groups are presented.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="77190b123add0efde06c44b4e0948b48" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":77943125,"asset_id":66935659,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/77943125/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="66935659"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="66935659"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 66935659; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> </div><div class="profile--tab_content_container js-tab-pane tab-pane" data-section-id="13563577" id="papers"><div class="js-work-strip profile--work_container" data-work-id="83227340"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" rel="nofollow" href="https://www.academia.edu/83227340/Some_criteria_for_the_Cohen_Macaulay_property_and_local_cohomology"><img alt="Research paper thumbnail of Some criteria for the Cohen-Macaulay property and local cohomology" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" rel="nofollow" href="https://www.academia.edu/83227340/Some_criteria_for_the_Cohen_Macaulay_property_and_local_cohomology">Some criteria for the Cohen-Macaulay property and local cohomology</a></div><div class="wp-workCard_item"><span>Acta Mathematica Sinica, English Series</span><span>, 2009</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">ABSTRACT Let a be an ideal of a commutative Noetherian ring R and M be a finitely generated R-mod...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">ABSTRACT Let a be an ideal of a commutative Noetherian ring R and M be a finitely generated R-module of dimension d. We characterize Cohen-Macaulay rings in term of a special homological dimension. Lastly, we prove that if R is a complete local ring, then the Matlis dual of top local cohomology module H a d (M) is a Cohen-Macaulay R-module provided that the R-module M satisfies some conditions.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="83227340"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="83227340"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 83227340; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=83227340]").text(description); $(".js-view-count[data-work-id=83227340]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 83227340; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='83227340']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=83227340]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":83227340,"title":"Some criteria for the Cohen-Macaulay property and local cohomology","internal_url":"https://www.academia.edu/83227340/Some_criteria_for_the_Cohen_Macaulay_property_and_local_cohomology","owner_id":194013305,"coauthors_can_edit":true,"owner":{"id":194013305,"first_name":"Amir","middle_initials":null,"last_name":"Mafi","page_name":"AmirMafi2","domain_name":"independent","created_at":"2021-05-22T06:14:23.216-07:00","display_name":"Amir Mafi","url":"https://independent.academia.edu/AmirMafi2"},"attachments":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="71947427"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/71947427/Results_on_Almost_Cohen_Macaulay_Modules"><img alt="Research paper thumbnail of Results on Almost Cohen-Macaulay Modules" class="work-thumbnail" src="https://attachments.academia-assets.com/81081301/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/71947427/Results_on_Almost_Cohen_Macaulay_Modules">Results on Almost Cohen-Macaulay Modules</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Let (R, m) be a commutative Noetherian local ring, and M be a non-zero finitely-generated R-modul...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Let (R, m) be a commutative Noetherian local ring, and M be a non-zero finitely-generated R-module. We show that if R is almost Cohen-Macaulay and M is perfect with finite projective dimension, then M is an almost Cohen-Macaulay module. Also, we give some necessary and sufficient conditions on M to be an almost Cohen-Macaulay module, by using Ext functors.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="41d67b39a9b6a2332833f586b35ec589" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":81081301,"asset_id":71947427,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/81081301/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="71947427"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="71947427"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 71947427; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="71947419"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" rel="nofollow" href="https://www.academia.edu/71947419/A_New_Characterization_of_Commutative_Artinian_Rings"><img alt="Research paper thumbnail of A New Characterization of Commutative Artinian Rings" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" rel="nofollow" href="https://www.academia.edu/71947419/A_New_Characterization_of_Commutative_Artinian_Rings">A New Characterization of Commutative Artinian Rings</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Abstract. Let R be a commutative Noetherian ring. It is shown that R is Artinian if and only if e...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Abstract. Let R be a commutative Noetherian ring. It is shown that R is Artinian if and only if every R-module is good, if and only if every R-module is representable. As a result, it follows that every nonzero submodule of any representable R-module is representable if and only if R is Artinian. This provides an answer to a question which is investigated in [1]. 1.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="71947419"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="71947419"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 71947419; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=71947419]").text(description); $(".js-view-count[data-work-id=71947419]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 71947419; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='71947419']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=71947419]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":71947419,"title":"A New Characterization of Commutative Artinian Rings","internal_url":"https://www.academia.edu/71947419/A_New_Characterization_of_Commutative_Artinian_Rings","owner_id":194013305,"coauthors_can_edit":true,"owner":{"id":194013305,"first_name":"Amir","middle_initials":null,"last_name":"Mafi","page_name":"AmirMafi2","domain_name":"independent","created_at":"2021-05-22T06:14:23.216-07:00","display_name":"Amir Mafi","url":"https://independent.academia.edu/AmirMafi2"},"attachments":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="71947360"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/71947360/Sequentially_Cohen_Macaulay_matroidal_ideals"><img alt="Research paper thumbnail of Sequentially Cohen-Macaulay matroidal ideals" class="work-thumbnail" src="https://attachments.academia-assets.com/81081254/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/71947360/Sequentially_Cohen_Macaulay_matroidal_ideals">Sequentially Cohen-Macaulay matroidal ideals</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Let R=K[x_1,...,x_n] be the polynomial ring in n variables over a field K and let J be a matroida...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Let R=K[x_1,...,x_n] be the polynomial ring in n variables over a field K and let J be a matroidal ideal of degree d in R. In this paper, we study the class of sequentially Cohen-Macaulay matroidal ideals. In particular, all sequentially Cohen-Macaulay matroidal ideals of degree 2 are classified. Furthermore, we give a classification of sequentially Cohen-Macaulay matroidal ideals of degree d≥ 3 in some special cases.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="ba9614012e3b5fd83bc3076e444de1cf" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":81081254,"asset_id":71947360,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/81081254/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="71947360"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="71947360"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 71947360; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="66935677"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/66935677/Sequentially_cohen_macaulay_matroidal_ideals"><img alt="Research paper thumbnail of Sequentially cohen-macaulay matroidal ideals" class="work-thumbnail" src="https://attachments.academia-assets.com/77943114/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/66935677/Sequentially_cohen_macaulay_matroidal_ideals">Sequentially cohen-macaulay matroidal ideals</a></div><div class="wp-workCard_item"><span>Filomat</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Let R = K[x1,...,xn] be the polynomial ring in n variables over a field K and let I be a matroida...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Let R = K[x1,...,xn] be the polynomial ring in n variables over a field K and let I be a matroidal ideal of degree d in R. Our main focus is determining when matroidal ideals are sequentially Cohen- Macaulay. In particular, all sequentially Cohen-Macaulay matroidal ideals of degree 2 are classified. Furthermore, we give a classification of sequentially Cohen-Macaulay matroidal ideals of degree d ? 3 in some special cases.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="5700a99e1063e4be292e5406998df89e" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":77943114,"asset_id":66935677,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/77943114/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="66935677"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="66935677"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 66935677; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="66935676"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/66935676/The_saturation_number_of_powers_of_graded_ideals"><img alt="Research paper thumbnail of The saturation number of powers of graded ideals" class="work-thumbnail" src="https://attachments.academia-assets.com/77943041/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/66935676/The_saturation_number_of_powers_of_graded_ideals">The saturation number of powers of graded ideals</a></div><div class="wp-workCard_item"><span>arXiv: Commutative Algebra</span><span>, 2019</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Let $S=K[x_1,\ldots,x_n]$ be the polynomial ring in $n$ variables over a field $K$ with maximal i...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Let $S=K[x_1,\ldots,x_n]$ be the polynomial ring in $n$ variables over a field $K$ with maximal ideal $\frak{m}=(x_1,...,x_n)$, and let $I$ be a graded ideal of $S$. In this paper, we define the saturation number $\sat(I)$ of $I$ to be the smallest non-negative integer $k$ such that $I:\mm^{k+1}= I:\mm^k$. We show that $f(k)$ is linearly bounded, and that $f(k)$ is a quasi-linear function for $k\gg 0$, if $I$ is a monomial ideal. Furthermore, we show that $\sat(I^k)=k$ if $I$ is a principal Borel ideal and prove that $\sat(I_{d,n}^k) =\max\{l\:\; (kd-l)/(k-l) \leq n\},$ where $I_{d,n}$ is the squarefree Veronese ideal generated in degree $d$. \end{abstract}</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="26509d11f7faa0878b8c8cac70752269" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":77943041,"asset_id":66935676,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/77943041/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="66935676"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="66935676"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 66935676; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="66935675"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/66935675/On_the_first_generalized_Hilbert_coefficient_and_depth_of_associated_graded_rings"><img alt="Research paper thumbnail of On the first generalized Hilbert coefficient and depth of associated graded rings" class="work-thumbnail" src="https://attachments.academia-assets.com/77943038/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/66935675/On_the_first_generalized_Hilbert_coefficient_and_depth_of_associated_graded_rings">On the first generalized Hilbert coefficient and depth of associated graded rings</a></div><div class="wp-workCard_item"><span>arXiv: Commutative Algebra</span><span>, 2017</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Let $(R,\mathfrak{m})$ be a $d$-dimensional Cohen-Macaulay local ring with infinite residue field...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Let $(R,\mathfrak{m})$ be a $d$-dimensional Cohen-Macaulay local ring with infinite residue field. Let $I$ be an ideal of $R$ that has analytic spread $\ell(I)=d$, satisfies the $G_d$ condition, the weak Artin-Nagata property $AN_{d-2}^-$ and depth$(R/I)\geq\min\lbrace 1,\dim R/I \rbrace$. In this paper, we show that if $j_1(I) = \lambda (I/J) +\lambda [R/(J_{d-1} :_{R} I+(J_{d-2} :_{R}I+I) :_R, \mathfrak{m}^\infty)]+1$, then depth$(G(I))\geq d -1$ and $r_J(I)\leq 2$, where $J$ is a general minimal reduction of $I$. In addition, we extend the result by Sally who has studied the depth of associated graded rings and minimal reductions for an $,\mathfrak{m}$-primary ideals.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="ebd24b6b8e24b1fa873e8adf5db6c794" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":77943038,"asset_id":66935675,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/77943038/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="66935675"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="66935675"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 66935675; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="66935674"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/66935674/On_the_Annihilation_of_local_homology_modules"><img alt="Research paper thumbnail of On the Annihilation of local homology modules" class="work-thumbnail" src="https://attachments.academia-assets.com/77943036/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/66935674/On_the_Annihilation_of_local_homology_modules">On the Annihilation of local homology modules</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Let a ⊆ b be two ideals of commutative Noetherian ring R and A an Artinian R-module. For a non-ne...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Let a ⊆ b be two ideals of commutative Noetherian ring R and A an Artinian R-module. For a non-negative integer n, we show that up+q=n Ann(Torp (R/b, H q (A))) ⊆ Ann(Torn (R/b, A)). As an immediate consequence, if H i (A) is Artinian for all i &lt; n then a ⊆ Rad(Ann(H i (A))) for all i &lt; n. Moreover, we prove that if a = (x1, . . . , xn) and c = ∩t≥1∩i=0Ann(Tori (R/a, A)), then c ⊆ ∩n−1 i=0 Ann(H a i (A)) where k = (n[n 2 ]).</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="4371d99cfb602a5b0d562c7c8b3e110b" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":77943036,"asset_id":66935674,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/77943036/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="66935674"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="66935674"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 66935674; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="66935673"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" rel="nofollow" href="https://www.academia.edu/66935673/Results_on_Generalization_of_Burch_s_Inequality_and_the_Depth_of_Rees_Algebra_and_Associated_Graded_Rings_of_an_Ideal_with_Respect_to_a_Cohen_Macaulay_Module"><img alt="Research paper thumbnail of Results on Generalization of Burch’s Inequality and the Depth of Rees Algebra and Associated Graded Rings of an Ideal with Respect to a Cohen-Macaulay Module" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" rel="nofollow" href="https://www.academia.edu/66935673/Results_on_Generalization_of_Burch_s_Inequality_and_the_Depth_of_Rees_Algebra_and_Associated_Graded_Rings_of_an_Ideal_with_Respect_to_a_Cohen_Macaulay_Module">Results on Generalization of Burch’s Inequality and the Depth of Rees Algebra and Associated Graded Rings of an Ideal with Respect to a Cohen-Macaulay Module</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Let be a local Cohen-Macaulay ring with infinite residue field, an Cohen - Macaulay module and ...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Let be a local Cohen-Macaulay ring with infinite residue field, an Cohen - Macaulay module and an ideal of Consider and , respectively, the Rees Algebra and associated graded ring of , and denote by the analytic spread of Burch’s inequality says that and equality holds if is Cohen-Macaulay. Thus, in that case one can compute the depth of associated graded ring of as In this paper we extend results in case of rings and ideals to the case of modules and we show that for associated graded module of with respect to i.e, , such an equality is also valid when is not necessarily Cohen-Macaulay, and we extend Burch’s inequality to modules. Also, we compute the Rees Algebra and associated graded ring of generically complete intersection of an ideal with respect to module in local Cohen - Macaulay ring and we obtain positive results for ideals with analytic deviation less or equal than one and reduction number at most two with respect to module</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="66935673"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="66935673"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 66935673; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=66935673]").text(description); $(".js-view-count[data-work-id=66935673]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 66935673; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='66935673']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=66935673]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":66935673,"title":"Results on Generalization of Burch’s Inequality and the Depth of Rees Algebra and Associated Graded Rings of an Ideal with Respect to a Cohen-Macaulay Module","internal_url":"https://www.academia.edu/66935673/Results_on_Generalization_of_Burch_s_Inequality_and_the_Depth_of_Rees_Algebra_and_Associated_Graded_Rings_of_an_Ideal_with_Respect_to_a_Cohen_Macaulay_Module","owner_id":194013305,"coauthors_can_edit":true,"owner":{"id":194013305,"first_name":"Amir","middle_initials":null,"last_name":"Mafi","page_name":"AmirMafi2","domain_name":"independent","created_at":"2021-05-22T06:14:23.216-07:00","display_name":"Amir Mafi","url":"https://independent.academia.edu/AmirMafi2"},"attachments":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="66935670"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/66935670/Almost_Cohen_Macaulayness_of_Koszul_Homology"><img alt="Research paper thumbnail of Almost Cohen-Macaulayness of Koszul Homology" class="work-thumbnail" src="https://attachments.academia-assets.com/77943035/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/66935670/Almost_Cohen_Macaulayness_of_Koszul_Homology">Almost Cohen-Macaulayness of Koszul Homology</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Let (R,m) be a commutative Noetherian ring, I an ideal of R and M a non-zero finitely generated R...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Let (R,m) be a commutative Noetherian ring, I an ideal of R and M a non-zero finitely generated R-module. We show that if M and H0(I,M) are aCM R-modules and I = (x1, . . . , xn+1) such that x1, . . . , xn is an M -regular sequence, then Hi(I,M) is an aCM R-module for all i. Moreover, we prove that if R and Hi(I, R) are aCM for all i, then R/(0 : I) is aCM. In addition, we prove that if R is aCM and x1, . . . , xn is an aCM d-sequence, then depthHi(x1, . . . , xn;R) ≥ i− 1 for all i.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="6146a1c5837d9bfff1b43036610445ff" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":77943035,"asset_id":66935670,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/77943035/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="66935670"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="66935670"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 66935670; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="66935669"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" rel="nofollow" href="https://www.academia.edu/66935669/Linear_resolutions_and_polymatroidal_ideals"><img alt="Research paper thumbnail of Linear resolutions and polymatroidal ideals" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" rel="nofollow" href="https://www.academia.edu/66935669/Linear_resolutions_and_polymatroidal_ideals">Linear resolutions and polymatroidal ideals</a></div><div class="wp-workCard_item"><span>Proceedings - Mathematical Sciences</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="66935669"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="66935669"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 66935669; 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Если $M$ - максимальный $R$-модуль Коэна-Маколея, то для достаточно больших $n$ и $1\le i\le d$ длины модулей $\operatorname{Ext}^i_R(R/J,M/I^nM)$ и $\operatorname{Tor}_i^R(R/J,M/I^nM)$ - полиномы степени $d-1$. Кроме того, показано, что $$ \operatorname{deg}\beta_i^R(M/I^nM) =\operatorname{deg}\mu^i_R(M/I^nM)=d-1, $$ где $\beta_i^R( \cdot )$ и $\mu^i_R( \cdot )$ - $i$-е число Бетти и $i$-е число Басса, соответственно. Библиография: 14 названий.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="66935668"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="66935668"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 66935668; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=66935668]").text(description); $(".js-view-count[data-work-id=66935668]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 66935668; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='66935668']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=66935668]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":66935668,"title":"О степени гильбертовых полиномов производных функторов","internal_url":"https://www.academia.edu/66935668/%D0%9E_%D1%81%D1%82%D0%B5%D0%BF%D0%B5%D0%BD%D0%B8_%D0%B3%D0%B8%D0%BB%D1%8C%D0%B1%D0%B5%D1%80%D1%82%D0%BE%D0%B2%D1%8B%D1%85_%D0%BF%D0%BE%D0%BB%D0%B8%D0%BD%D0%BE%D0%BC%D0%BE%D0%B2_%D0%BF%D1%80%D0%BE%D0%B8%D0%B7%D0%B2%D0%BE%D0%B4%D0%BD%D1%8B%D1%85_%D1%84%D1%83%D0%BD%D0%BA%D1%82%D0%BE%D1%80%D0%BE%D0%B2","owner_id":194013305,"coauthors_can_edit":true,"owner":{"id":194013305,"first_name":"Amir","middle_initials":null,"last_name":"Mafi","page_name":"AmirMafi2","domain_name":"independent","created_at":"2021-05-22T06:14:23.216-07:00","display_name":"Amir Mafi","url":"https://independent.academia.edu/AmirMafi2"},"attachments":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="66935667"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" rel="nofollow" href="https://www.academia.edu/66935667/Gorenstein_homological_dimension_and_Ext_depth_of_modules"><img alt="Research paper thumbnail of Gorenstein homological dimension and Ext-depth of modules" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" rel="nofollow" href="https://www.academia.edu/66935667/Gorenstein_homological_dimension_and_Ext_depth_of_modules">Gorenstein homological dimension and Ext-depth of modules</a></div><div class="wp-workCard_item"><span>Bulletin of the Belgian Mathematical Society - Simon Stevin</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">ABSTRACT Let $(R,{\frak{m}},k)$ be a commutative Noetherian local ring. It is well-known that $R$...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">ABSTRACT Let $(R,{\frak{m}},k)$ be a commutative Noetherian local ring. It is well-known that $R$ is regular if and only if the flat dimension of $k$ is finite. In this paper, we show that $R$ is Gorenstein if and only if the Gorenstein flat dimension of $k$ is finite. Also, we will show that if $R$ is a Cohen-Macaulay ring and $M$ is a Tor-finite $R$-module of finite Gorenstein flat dimension, then the depth of the ring is equal to the sum of the Gorenstein flat dimension and Ext-depth of $M$. As a consequence, we get that this formula holds for every syzygy of a finitely generated $R$-module over a Gorenstein local ring.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="66935667"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="66935667"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 66935667; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=66935667]").text(description); $(".js-view-count[data-work-id=66935667]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 66935667; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='66935667']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=66935667]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":66935667,"title":"Gorenstein homological dimension and Ext-depth of modules","internal_url":"https://www.academia.edu/66935667/Gorenstein_homological_dimension_and_Ext_depth_of_modules","owner_id":194013305,"coauthors_can_edit":true,"owner":{"id":194013305,"first_name":"Amir","middle_initials":null,"last_name":"Mafi","page_name":"AmirMafi2","domain_name":"independent","created_at":"2021-05-22T06:14:23.216-07:00","display_name":"Amir Mafi","url":"https://independent.academia.edu/AmirMafi2"},"attachments":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="66935665"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/66935665/On_stability_properties_of_powers_of_polymatroidal_ideals"><img alt="Research paper thumbnail of On stability properties of powers of polymatroidal ideals" class="work-thumbnail" src="https://attachments.academia-assets.com/77943116/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/66935665/On_stability_properties_of_powers_of_polymatroidal_ideals">On stability properties of powers of polymatroidal ideals</a></div><div class="wp-workCard_item"><span>Collectanea Mathematica</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Let R = K[x 1 , ..., x n ] be the polynomial ring in n variables over a field K with the maximal ...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Let R = K[x 1 , ..., x n ] be the polynomial ring in n variables over a field K with the maximal ideal m = (x 1 , ..., x n). Let astab(I) and dstab(I) be the smallest integer n for which Ass(I n) and depth(I n) stabilize, respectively. In this paper we show that astab(I) = dstab(I) in the following cases: (i) I is a matroidal ideal and n ≤ 5. (ii) I is a polymatroidal ideal, n = 4 and m / ∈ Ass ∞ (I), where Ass ∞ (I) is the stable set of associated prime ideals of I. (iii) I is a polymatroidal ideal of degree 2. Moreover, we give an example of a polymatroidal ideal for which astab(I) = dstab(I). This is a counterexample to the conjecture of Herzog and Qureshi, according to which these two numbers are the same for polymatroidal ideals.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="9f919f7c28489fceac8d91e0129c1ac1" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":77943116,"asset_id":66935665,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/77943116/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="66935665"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="66935665"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 66935665; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="66935664"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/66935664/Effect_of_Perioperative_Management_on_Outcome_of_Patients_after_Craniosynostosis_Surgery"><img alt="Research paper thumbnail of Effect of Perioperative Management on Outcome of Patients after Craniosynostosis Surgery" class="work-thumbnail" src="https://attachments.academia-assets.com/77943111/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/66935664/Effect_of_Perioperative_Management_on_Outcome_of_Patients_after_Craniosynostosis_Surgery">Effect of Perioperative Management on Outcome of Patients after Craniosynostosis Surgery</a></div><div class="wp-workCard_item"><span>World journal of plastic surgery</span><span>, 2017</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Craniosynostosis results from premature closure of one or more cranial sutures, leading to deform...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Craniosynostosis results from premature closure of one or more cranial sutures, leading to deformed calvaria and craniofacial skeleton at birth. Postoperative complications and outcome in intensive care unit (ICU) is related to surgical method and perioperative management. This study determined the perioperative risk factors, which affect outcome of patients after craniosynostosis surgery. In a retrospective study, 178 patients with craniosynostosis who underwent primary cranial reconstruction were included. Postoperative complications following neurosurgical procedures including fever in ICU, level of consciousness, re-intubation, and blood, urine, and other cultures were also performed and their association with the main outcomes (length of ICU stay) were analyzed. Factors independently associated with a longer pediatric ICU stay were fever (OR=1.59, 95% CI=1.25-4.32; p=0.001), perioperative bleeding (OR=2.25, 95% CI=1.65-3.65; p=0.01), age (having surgery after the first 5 years)...</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="1f86a304985580dcad8105fb8aa0ccdf" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":77943111,"asset_id":66935664,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/77943111/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="66935664"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="66935664"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 66935664; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="66935663"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/66935663/On_the_finiteness_of_local_homology_modules"><img alt="Research paper thumbnail of On the finiteness of local homology modules" class="work-thumbnail" src="https://attachments.academia-assets.com/77943110/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/66935663/On_the_finiteness_of_local_homology_modules">On the finiteness of local homology modules</a></div><div class="wp-workCard_item"><span>Rendiconti Del Seminario Matematico</span><span>, 2009</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Let (R,m) be a commutative Noetherian complete local ring, a an ideal of R, and A an Artinian R-m...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Let (R,m) be a commutative Noetherian complete local ring, a an ideal of R, and A an Artinian R-module with N-dim A = d. We prove that if d > 0, then Cosupp(H a d−1 (A)) is finite and if d ≤ 3, then the set Coass(H a i (A)) is finite for all i. Moreover, if either d ≤ 2 or the cohomological dimension cd(a) = 1 then H a i (A) is a-coartinian for all i; that is, Tor R j (R/a,H a i (A)) is Artinian for all i, j. We also show that if H a i (A) is a-coartinian for all i < n, then Tor R j (R/a,H a n (A)) is Artinian for j = 0,1. In particular, the set Coass(H a n (A)) is finite.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="1054e32c642c50cb2477f6235a55869d" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":77943110,"asset_id":66935663,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/77943110/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="66935663"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="66935663"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 66935663; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="66935662"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/66935662/Top_generalized_local_cohomology_modules"><img alt="Research paper thumbnail of Top generalized local cohomology modules" class="work-thumbnail" src="https://attachments.academia-assets.com/77943031/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/66935662/Top_generalized_local_cohomology_modules">Top generalized local cohomology modules</a></div><div class="wp-workCard_item"><span>Turkish Journal of Mathematics</span><span>, 2011</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Let (R, Ñ) be a commutative Noetherian local ring and M , N two non-zero finitely generated Rmodu...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Let (R, Ñ) be a commutative Noetherian local ring and M , N two non-zero finitely generated Rmodules with pd(M) = n < ∞ and dim(N) = d. In this paper, we show that if the top generalized local cohomology module H n+d Ñ (M, N) = 0 , then the following statements are equivalent: (i) Ann(0 : H d m (N) Ô) = Ô for all Ô ∈ Var(Ann(H d Ñ (N))) ; (ii) Ann(0 : H n+d m (M,N) Ô) = Ô for all Ô ∈ Var(Ann(H n+d Ñ (M, N))) .</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="b091e5c3c597a022761855cad765d979" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":77943031,"asset_id":66935662,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/77943031/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="66935662"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="66935662"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 66935662; 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Some basic properties an...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">In this paper we study the class of sequentially Cohen-Macaulay modules. 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