CINXE.COM

<!DOCTYPE html> <html prefix=" dbp: http://dbpedia.org/property/ dbo: http://dbedia.org/ontology/ dct: http://purl.org/dc/terms/ dbd: http://dbpedia.org/datatype/ og: https://ogp.me/ns# " >  <head> <meta charset="utf-8" /> <meta name="viewport" content="width=device-width, initial-scale=1" /> <title>About: Injective module</title>  <link rel="alternate" type="application/rdf+xml" href="http://dbpedia.org/data/Injective_module.rdf" title="Structured Descriptor Document (RDF/XML format)" /> <link rel="alternate" type="text/n3" href="http://dbpedia.org/data/Injective_module.n3" title="Structured Descriptor Document (N3 format)" /> <link rel="alternate" type="text/turtle" href="http://dbpedia.org/data/Injective_module.ttl" title="Structured Descriptor Document (Turtle format)" /> <link rel="alternate" type="application/json+rdf" href="http://dbpedia.org/data/Injective_module.jrdf" title="Structured Descriptor Document (RDF/JSON format)" /> <link rel="alternate" type="application/json" href="http://dbpedia.org/data/Injective_module.json" title="Structured Descriptor Document (RDF/JSON format)" /> <link rel="alternate" type="application/atom+xml" href="http://dbpedia.org/data/Injective_module.atom" title="OData (Atom+Feed format)" /> <link rel="alternate" type="text/plain" href="http://dbpedia.org/data/Injective_module.ntriples" title="Structured Descriptor Document (N-Triples format)" /> <link rel="alternate" type="text/csv" href="http://dbpedia.org/sparql?default-graph-uri=http%3A%2F%2Fdbpedia.org&query=DESCRIBE%20%3Chttp%3A%2F%2Fdbpedia.org%2Fresource%2FInjective_module%3E&format=text%2Fcsv" title="Structured Descriptor Document (CSV format)" /> <link rel="alternate" type="application/microdata+json" href="http://dbpedia.org/sparql?default-graph-uri=http%3A%2F%2Fdbpedia.org&query=DESCRIBE%20%3Chttp%3A%2F%2Fdbpedia.org%2Fresource%2FInjective_module%3E&format=application%2Fmicrodata%2Bjson" title="Structured Descriptor Document (Microdata/JSON format)" /> <link rel="alternate" type="text/html" href="http://dbpedia.org/sparql?default-graph-uri=http%3A%2F%2Fdbpedia.org&query=DESCRIBE%20%3Chttp%3A%2F%2Fdbpedia.org%2Fresource%2FInjective_module%3E&format=text%2Fhtml" title="Structured Descriptor Document (Microdata/HTML format)" /> <link rel="alternate" type="application/ld+json" href="http://dbpedia.org/sparql?default-graph-uri=http%3A%2F%2Fdbpedia.org&query=DESCRIBE%20%3Chttp%3A%2F%2Fdbpedia.org%2Fresource%2FInjective_module%3E&format=application%2Fld%2Bjson" title="Structured Descriptor Document (JSON-LD format)" /> <link rel="alternate" type="text/x-html-script-ld+json" href="http://dbpedia.org/sparql?default-graph-uri=http%3A%2F%2Fdbpedia.org&query=DESCRIBE%20%3Chttp%3A%2F%2Fdbpedia.org%2Fresource%2FInjective_module%3E&format=text%2Fx-html-script-ld%2Bjson" title="Structured Descriptor Document (HTML with embedded JSON-LD)" /> <link rel="alternate" type="text/x-html-script-turtle" href="http://dbpedia.org/sparql?default-graph-uri=http%3A%2F%2Fdbpedia.org&query=DESCRIBE%20%3Chttp%3A%2F%2Fdbpedia.org%2Fresource%2FInjective_module%3E&format=text%2Fx-html-script-turtle" title="Structured Descriptor Document (HTML with embedded Turtle)" /> <link rel="timegate" type="text/html" href="http://dbpedia.mementodepot.org/timegate/http://dbpedia.org/page/Injective_module" title="Time Machine" /> <link rel="foaf:primarytopic" href="http://dbpedia.org/resource/Injective_module"/> <link rev="describedby" href="http://dbpedia.org/resource/Injective_module"/>   <link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/bootstrap/5.2.1/css/bootstrap.min.css" integrity="sha512-siwe/oXMhSjGCwLn+scraPOWrJxHlUgMBMZXdPe2Tnk3I0x3ESCoLz7WZ5NTH6SZrywMY+PB1cjyqJ5jAluCOg==" crossorigin="anonymous" /> <link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/bootstrap-icons/1.9.1/font/bootstrap-icons.min.css" integrity="sha512-5PV92qsds/16vyYIJo3T/As4m2d8b6oWYfoqV+vtizRB6KhF1F9kYzWzQmsO6T3z3QG2Xdhrx7FQ+5R1LiQdUA==" crossorigin="anonymous" />    <meta property="og:title" content="Injective module" /> <meta property="og:type" content="article" /> <meta property="og:url" content="http://dbpedia.org/resource/Injective_module" /> <meta property="og:image" content="http://commons.wikimedia.org/wiki/Special:FilePath/Injective_module.svg?width=300" /> <meta property="og:description" content="In mathematics, especially in the area of abstract algebra known as module theory, an injective module is a module Q that shares certain desirable properties with the Z-module Q of all rational numbers. Specifically, if Q is a submodule of some other module, then it is already a direct summand of that module; also, given a submodule of a module Y, then any module homomorphism from this submodule to Q can be extended to a homomorphism from all of Y to Q. This concept is dual to that of projective modules. Injective modules were introduced in and are discussed in some detail in the textbook ." /> <meta property="og:site_name" content="DBpedia" />  </head> <body about="http://dbpedia.org/resource/Injective_module">  <nav class="navbar navbar-expand-md navbar-light bg-light fixed-top align-items-center"> <div class="container-xl"> <a class="navbar-brand" href="http://wiki.dbpedia.org/about" title="About DBpedia" style="color: #2c5078"> <img class="img-fluid" src="/statics/images/dbpedia_logo_land_120.png" alt="About DBpedia" /> </a> <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#dbp-navbar" aria-controls="dbp-navbar" aria-expanded="false" aria-label="Toggle navigation"> </button> <div class="collapse navbar-collapse" id="dbp-navbar"> <ul class="navbar-nav me-auto mb-2 mb-lg-0"> <li class="nav-item dropdown"> <a class="nav-link dropdown-toggle" href="#" id="navbarDropdownBrowse" role="button" data-bs-toggle="dropdown" aria-expanded="false"> Browse using</a> <ul class="dropdown-menu" aria-labelledby="navbarDropdownBrowse"> <li class="dropdown-item"><a class="nav-link" href="/describe/?uri=http%3A%2F%2Fdbpedia.org%2Fresource%2FInjective_module">OpenLink Faceted Browser</a></li> <li class="dropdown-item"><a class="nav-link" href="http://osde.demo.openlinksw.com/#/editor?uri=http%3A%2F%2Fdbpedia.org%2Fdata%2FInjective_module.ttl&view=statements">OpenLink Structured Data Editor</a></li> <li class="dropdown-item"><a class="nav-link" href="http://en.lodlive.it/?http%3A%2F%2Fdbpedia.org%2Fresource%2FInjective_module">LodLive Browser</a></li>  </ul> </li> <li class="nav-item dropdown"> <a class="nav-link dropdown-toggle" href="#" id="navbarDropdownFormats" role="button" data-bs-toggle="dropdown" aria-expanded="false"> Formats</a> <ul class="dropdown-menu" aria-labelledby="navbarDropdownFormats"> <li class="dropdown-item-text">RDF:</li> <li><a class="dropdown-item" href="http://dbpedia.org/data/Injective_module.ntriples">N-Triples</a></li> <li><a class="dropdown-item" href="http://dbpedia.org/data/Injective_module.n3">N3</a></li> <li><a class="dropdown-item" href="http://dbpedia.org/data/Injective_module.ttl">Turtle</a></li> <li><a class="dropdown-item" href="http://dbpedia.org/data/Injective_module.json">JSON</a></li> <li><a class="dropdown-item" href="http://dbpedia.org/data/Injective_module.rdf">XML</a></li> <li class="dropdown-divider"></li> <li class="dropdown-item-text">OData:</li> <li><a class="dropdown-item" href="http://dbpedia.org/data/Injective_module.atom">Atom</a></li> <li><a class="dropdown-item" href="http://dbpedia.org/data/Injective_module.jsod">JSON</a></li> <li class="dropdown-divider"></li> <li class="dropdown-item-text">Microdata:</li> <li><a class="dropdown-item" href="http://dbpedia.org/sparql?default-graph-uri=http%3A%2F%2Fdbpedia.org&query=DESCRIBE%20%3Chttp%3A%2F%2Fdbpedia.org%2Fresource%2FInjective_module%3E&format=application%2Fmicrodata%2Bjson">JSON</a></li> <li><a class="dropdown-item" href="http://dbpedia.org/sparql?default-graph-uri=http%3A%2F%2Fdbpedia.org&query=DESCRIBE%20%3Chttp%3A%2F%2Fdbpedia.org%2Fresource%2FInjective_module%3E&format=text%2Fhtml">HTML</a></li> <li class="dropdown-divider"></li> <li class="dropdown-item-text">Embedded:</li> <li><a class="dropdown-item" href="http://dbpedia.org/sparql?default-graph-uri=http%3A%2F%2Fdbpedia.org&query=DESCRIBE%20%3Chttp%3A%2F%2Fdbpedia.org%2Fresource%2FInjective_module%3E&format=text%2Fx-html-script-ld%2Bjson">JSON</a></li> <li><a class="dropdown-item" href="http://dbpedia.org/sparql?default-graph-uri=http%3A%2F%2Fdbpedia.org&query=DESCRIBE%20%3Chttp%3A%2F%2Fdbpedia.org%2Fresource%2FInjective_module%3E&format=text%2Fx-html-script-turtle">Turtle</a></li> <li class="dropdown-divider"></li> <li class="dropdown-item-text">Other:</li> <li><a class="dropdown-item" href="http://dbpedia.org/sparql?default-graph-uri=http%3A%2F%2Fdbpedia.org&query=DESCRIBE%20%3Chttp%3A%2F%2Fdbpedia.org%2Fresource%2FInjective_module%3E&format=text%2Fcsv">CSV</a></li> <li><a class="dropdown-item" href="http://dbpedia.org/sparql?default-graph-uri=http%3A%2F%2Fdbpedia.org&query=DESCRIBE%20%3Chttp%3A%2F%2Fdbpedia.org%2Fresource%2FInjective_module%3E&format=application%2Fld%2Bjson">JSON-LD</a></li> </ul> </li> </ul> <ul class="navbar-nav ms-auto"> <li class="nav-item"> <a class="nav-link" href="/fct/" title="Switch to /fct endpoint"> Faceted Browser </a> </li> <li class="nav-item"> <a class="nav-link" href="/sparql/" title="Switch to /sparql endpoint"> Sparql Endpoint </a> </li> </ul> </div> </div> </nav> <div style="margin-bottom: 60px"></div>   <section> <div class="container-xl"> <div class="row"> <div class="col"> <h1 id="title" class="display-6">About: <a href="http://dbpedia.org/resource/Injective_module">Injective module</a> </h1> </div> </div> <div class="row"> <div class="col"> <div class="text-muted"> An Entity of Type: <a href="http://dbpedia.org/ontology/Work">work</a>, from Named Graph: <a href="http://dbpedia.org">http://dbpedia.org</a>, within Data Space: <a href="http://dbpedia.org">dbpedia.org</a> </div> </div> </div> <div class="row pt-2"> <div class="col-xs-9 col-sm-10"> In mathematics, especially in the area of abstract algebra known as module theory, an injective module is a module Q that shares certain desirable properties with the Z-module Q of all rational numbers. Specifically, if Q is a submodule of some other module, then it is already a direct summand of that module; also, given a submodule of a module Y, then any module homomorphism from this submodule to Q can be extended to a homomorphism from all of Y to Q. This concept is dual to that of projective modules. Injective modules were introduced in and are discussed in some detail in the textbook . </div> <div class="col-xs-3 col-sm-2"> <a href="#" class="thumbnail"> <img src="http://commons.wikimedia.org/wiki/Special:FilePath/Injective_module.svg?width=300" alt="thumbnail" class="img-fluid" /> </a> </div> </div> </div> </section>   <section> <div class="container-xl"> <div class="row"> <div class="table-responsive"> <table class="table table-hover table-sm table-light"> <thead> <tr> <th class="col-xs-3 ">Property</th> <th class="col-xs-9 px-3">Value</th> </tr> </thead> <tbody> <tr class="odd"><td class="col-2"><a class="uri" href="http://dbpedia.org/ontology/abstract">dbo:abstract</a> </td><td class="col-10 text-break"><ul> <li>In mathematics, especially in the area of abstract algebra known as module theory, an injective module is a module Q that shares certain desirable properties with the Z-module Q of all rational numbers. Specifically, if Q is a submodule of some other module, then it is already a direct summand of that module; also, given a submodule of a module Y, then any module homomorphism from this submodule to Q can be extended to a homomorphism from all of Y to Q. This concept is dual to that of projective modules. Injective modules were introduced in and are discussed in some detail in the textbook . Injective modules have been heavily studied, and a variety of additional notions are defined in terms of them: Injective cogenerators are injective modules that faithfully represent the entire category of modules. Injective resolutions measure how far from injective a module is in terms of the and represent modules in the derived category. Injective hulls are maximal essential extensions, and turn out to be minimal injective extensions. Over a Noetherian ring, every injective module is uniquely a direct sum of indecomposable modules, and their structure is well understood. An injective module over one ring, may not be injective over another, but there are well-understood methods of changing rings which handle special cases. Rings which are themselves injective modules have a number of interesting properties and include rings such as group rings of finite groups over fields. Injective modules include divisible groups and are generalized by the notion of injective objects in category theory. (en)</li> <li style="display:none;">En matemáticas, un módulo inyectivo es un módulo Q que comparte ciertas propiedades deseables con el Z-módulo Q de todos los números racionales. Específicamente, si Q es un submódulo de algún otro módulo, entonces es un sumando directo de ese módulo; también, dado un submódulo de un módulo Y, entonces cualquier homomorfismo de módulos de este submódulo a Q se puede ampliar a un homomorfismo de todo Y a Q. Este concepto es dual al de los módulos proyectivos. (es)</li> <li style="display:none;">En mathématiques, et plus spécifiquement en algèbre homologique, un module injectif est un module Q (à gauche par exemple) sur un anneau A tel que pour tout morphisme injectif f : X → Y entre deux A-modules (à gauche) et pour tout morphisme g : X → Q, il existe un morphisme h : Y → Q tel que hf = g, c'est-à-dire tel que le diagramme suivant commute : Autrement dit : Q est injectif si pour tout module Y, tout morphisme d'un sous-module de Y vers Q s'étend à Y. (fr)</li> <li style="display:none;">In matematica, un modulo iniettivo è un modulo con la proprietà di essere un addendo diretto di ogni modulo che lo contiene: ovvero Q è iniettivo se, per ogni modulo M che lo contiene, esiste un sottomodulo N di M tale che M è la somma diretta di N e Q. Questo concetto è il duale di quello di modulo proiettivo; è stato introdotto da nel 1940. Un esempio di modulo iniettivo è lo -modulo dei numeri razionali. (it)</li> <li style="display:none;">数学において、入射加群（にゅうしゃかぐん、英: injective module）、あるいは移入加群（いにゅうかぐん）とは、関手 Hom(–, E) が完全となるような加群 E のことである。ホモロジー代数における基本的な概念のひとつ。 (ja)</li> <li style="display:none;">환론에서 단사 가군(單射加群, 영어: injective module)은 이를 포함하는 모든 가군을 직합으로 쪼갤 수 있는 가군이다. 가군의 범주에서의 단사 대상이다. (ko)</li> <li style="display:none;">Инъекти́вный мо́дуль — одно из основных понятий гомологической алгебры. Модуль над кольцом (как правило, считаемым ассоциативным с единичным элементом) называется инъективным, если для всякого гомоморфизма и мономорфизма (инъективного гомоморфизма) существует такой гомоморфизм , что , то есть данная диаграмма коммутативна: Можно указать ещё один критерий инъективности: инъективен тогда и только тогда, когда для любого мономорфизма индуцированный гомоморфизм является эпиморфизмом. Каждый модуль является подмодулем некоторого инъективного модуля. Эта теорема двойственна тому, что каждый модуль является гомоморфным образом проективного (даже свободного) модуля, хотя доказательство её более сложно. Прямое произведение модулей инъективно тогда и только тогда, когда инъективен каждый сомножитель. (ru)</li> <li style="display:none;">Ін'єктивний модуль — один з типів модулів, що є двоїстим до проєктивного модуля і широко використовується в гомологічній алгебрі і загалом в теорії кілець. (uk)</li> <li style="display:none;">內射模（英語：injective module），在模論中，是具有與有理數（視為 -模）相似性質的模。內射模是投射模的對偶概念，由Reinhold Baer於1940年引進。 (zh)</li> </ul></td></tr><tr class="even"><td class="col-2"><a class="uri" href="http://dbpedia.org/ontology/thumbnail">dbo:thumbnail</a> </td><td class="col-10 text-break"><ul> <li><a class="uri" rel="dbo:thumbnail" resource="http://commons.wikimedia.org/wiki/Special:FilePath/Injective_module.svg?width=300" href="http://commons.wikimedia.org/wiki/Special:FilePath/Injective_module.svg?width=300">wiki-commons:Special:FilePath/Injective_module.svg?width=300</a></li> </ul></td></tr><tr class="odd"><td class="col-2"><a class="uri" href="http://dbpedia.org/ontology/wikiPageExternalLink">dbo:wikiPageExternalLink</a> </td><td class="col-10 text-break"><ul> <li><a class="uri" rel="dbo:wikiPageExternalLink nofollow" resource="http://www.cms.math.ca/cjm/v15/p363" href="http://www.cms.math.ca/cjm/v15/p363">http://www.cms.math.ca/cjm/v15/p363</a></li> <li><a class="uri" rel="dbo:wikiPageExternalLink nofollow" resource="https://books.google.com/books%3Fid=PswhrD_wUIkC" href="https://books.google.com/books%3Fid=PswhrD_wUIkC">https://books.google.com/books%3Fid=PswhrD_wUIkC</a></li> <li><a class="uri" rel="dbo:wikiPageExternalLink nofollow" resource="https://archive.org/details/modulesstructure0000gola" href="https://archive.org/details/modulesstructure0000gola">https://archive.org/details/modulesstructure0000gola</a></li> </ul></td></tr><tr class="even"><td class="col-2"><a class="uri" href="http://dbpedia.org/ontology/wikiPageID">dbo:wikiPageID</a> </td><td class="col-10 text-break"><ul> <li>473775 (xsd:integer)</li> </ul></td></tr><tr class="odd"><td class="col-2"><a class="uri" href="http://dbpedia.org/ontology/wikiPageLength">dbo:wikiPageLength</a> </td><td class="col-10 text-break"><ul> <li>28511 (xsd:nonNegativeInteger)</li> </ul></td></tr><tr class="even"><td class="col-2"><a class="uri" href="http://dbpedia.org/ontology/wikiPageRevisionID">dbo:wikiPageRevisionID</a> </td><td class="col-10 text-break"><ul> <li>1121784240 (xsd:integer)</li> </ul></td></tr><tr class="odd"><td class="col-2"><a class="uri" href="http://dbpedia.org/ontology/wikiPageWikiLink">dbo:wikiPageWikiLink</a> </td><td class="col-10 text-break"><ul> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Prime_ideal" href="http://dbpedia.org/resource/Prime_ideal">dbr:Prime_ideal</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Principal_ideal_domain" href="http://dbpedia.org/resource/Principal_ideal_domain">dbr:Principal_ideal_domain</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Prüfer_group" href="http://dbpedia.org/resource/Prüfer_group">dbr:Prüfer_group</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Endomorphism_ring" href="http://dbpedia.org/resource/Endomorphism_ring">dbr:Endomorphism_ring</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Module_(mathematics)" href="http://dbpedia.org/resource/Module_(mathematics)">dbr:Module_(mathematics)</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Monomorphism" href="http://dbpedia.org/resource/Monomorphism">dbr:Monomorphism</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Category:Module_theory" href="http://dbpedia.org/resource/Category:Module_theory">dbc:Module_theory</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Archiv_der_Mathematik" href="http://dbpedia.org/resource/Archiv_der_Mathematik">dbr:Archiv_der_Mathematik</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Cyclic_module" href="http://dbpedia.org/resource/Cyclic_module">dbr:Cyclic_module</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Vector_space" href="http://dbpedia.org/resource/Vector_space">dbr:Vector_space</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Dedekind_domain" href="http://dbpedia.org/resource/Dedekind_domain">dbr:Dedekind_domain</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Derived_category" href="http://dbpedia.org/resource/Derived_category">dbr:Derived_category</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Derived_functor" href="http://dbpedia.org/resource/Derived_functor">dbr:Derived_functor</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Indecomposable_module" href="http://dbpedia.org/resource/Indecomposable_module">dbr:Indecomposable_module</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Injective_cogenerator" href="http://dbpedia.org/resource/Injective_cogenerator">dbr:Injective_cogenerator</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Injective_hull" href="http://dbpedia.org/resource/Injective_hull">dbr:Injective_hull</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Integral_domain" href="http://dbpedia.org/resource/Integral_domain">dbr:Integral_domain</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Quotient_ring" href="http://dbpedia.org/resource/Quotient_ring">dbr:Quotient_ring</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Ringed_space" href="http://dbpedia.org/resource/Ringed_space">dbr:Ringed_space</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Mathematics" href="http://dbpedia.org/resource/Mathematics">dbr:Mathematics</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Essential_extension" href="http://dbpedia.org/resource/Essential_extension">dbr:Essential_extension</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Noetherian_ring" href="http://dbpedia.org/resource/Noetherian_ring">dbr:Noetherian_ring</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Subring" href="http://dbpedia.org/resource/Subring">dbr:Subring</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Publicationes_Mathematicae_Debrecen" href="http://dbpedia.org/resource/Publicationes_Mathematicae_Debrecen">dbr:Publicationes_Mathematicae_Debrecen</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Pure_submodule" href="http://dbpedia.org/resource/Pure_submodule">dbr:Pure_submodule</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Quotient_module" href="http://dbpedia.org/resource/Quotient_module">dbr:Quotient_module</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Module_theory" href="http://dbpedia.org/resource/Module_theory">dbr:Module_theory</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Short_exact_sequence" href="http://dbpedia.org/resource/Short_exact_sequence">dbr:Short_exact_sequence</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Commutative_diagram" href="http://dbpedia.org/resource/Commutative_diagram">dbr:Commutative_diagram</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Commutative_ring" href="http://dbpedia.org/resource/Commutative_ring">dbr:Commutative_ring</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Frobenius_algebra" href="http://dbpedia.org/resource/Frobenius_algebra">dbr:Frobenius_algebra</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Functor_category" href="http://dbpedia.org/resource/Functor_category">dbr:Functor_category</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Ideal_(ring_theory)" href="http://dbpedia.org/resource/Ideal_(ring_theory)">dbr:Ideal_(ring_theory)</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Journal_of_Algebra" href="http://dbpedia.org/resource/Journal_of_Algebra">dbr:Journal_of_Algebra</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Divisible_group" href="http://dbpedia.org/resource/Divisible_group">dbr:Divisible_group</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Dual_(category_theory)" href="http://dbpedia.org/resource/Dual_(category_theory)">dbr:Dual_(category_theory)</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Linear_span" href="http://dbpedia.org/resource/Linear_span">dbr:Linear_span</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Local_ring" href="http://dbpedia.org/resource/Local_ring">dbr:Local_ring</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Field_(mathematics)" href="http://dbpedia.org/resource/Field_(mathematics)">dbr:Field_(mathematics)</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Flat_module" href="http://dbpedia.org/resource/Flat_module">dbr:Flat_module</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Formal_power_series" href="http://dbpedia.org/resource/Formal_power_series">dbr:Formal_power_series</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Direct_sum_of_modules" href="http://dbpedia.org/resource/Direct_sum_of_modules">dbr:Direct_sum_of_modules</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Coinduced_module" href="http://dbpedia.org/resource/Coinduced_module">dbr:Coinduced_module</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Product_(category_theory)" href="http://dbpedia.org/resource/Product_(category_theory)">dbr:Product_(category_theory)</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Projective_module" href="http://dbpedia.org/resource/Projective_module">dbr:Projective_module</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Resolution_(algebra)" href="http://dbpedia.org/resource/Resolution_(algebra)">dbr:Resolution_(algebra)</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Ring_(mathematics)" href="http://dbpedia.org/resource/Ring_(mathematics)">dbr:Ring_(mathematics)</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Finitely-generated_module" href="http://dbpedia.org/resource/Finitely-generated_module">dbr:Finitely-generated_module</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Category:Homological_algebra" href="http://dbpedia.org/resource/Category:Homological_algebra">dbc:Homological_algebra</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Abelian_group" href="http://dbpedia.org/resource/Abelian_group">dbr:Abelian_group</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Abstract_algebra" href="http://dbpedia.org/resource/Abstract_algebra">dbr:Abstract_algebra</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Academic_Press" href="http://dbpedia.org/resource/Academic_Press">dbr:Academic_Press</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Characteristic_(algebra)" href="http://dbpedia.org/resource/Characteristic_(algebra)">dbr:Characteristic_(algebra)</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Bimodule" href="http://dbpedia.org/resource/Bimodule">dbr:Bimodule</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Eben_Matlis" href="http://dbpedia.org/resource/Eben_Matlis">dbr:Eben_Matlis</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Hereditary_ring" href="http://dbpedia.org/resource/Hereditary_ring">dbr:Hereditary_ring</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Hom_functor" href="http://dbpedia.org/resource/Hom_functor">dbr:Hom_functor</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Module_homomorphism" href="http://dbpedia.org/resource/Module_homomorphism">dbr:Module_homomorphism</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Direct_summand" href="http://dbpedia.org/resource/Direct_summand">dbr:Direct_summand</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Artinian_ring" href="http://dbpedia.org/resource/Artinian_ring">dbr:Artinian_ring</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Associative_algebra" href="http://dbpedia.org/resource/Associative_algebra">dbr:Associative_algebra</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Bulletin_of_the_American_Mathematical_Society" href="http://dbpedia.org/resource/Bulletin_of_the_American_Mathematical_Society">dbr:Bulletin_of_the_American_Mathematical_Society</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Polynomial_ring" href="http://dbpedia.org/resource/Polynomial_ring">dbr:Polynomial_ring</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Circle_group" href="http://dbpedia.org/resource/Circle_group">dbr:Circle_group</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Field_of_fractions" href="http://dbpedia.org/resource/Field_of_fractions">dbr:Field_of_fractions</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Free_module" href="http://dbpedia.org/resource/Free_module">dbr:Free_module</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Contravariant_functor" href="http://dbpedia.org/resource/Contravariant_functor">dbr:Contravariant_functor</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Group_representation" href="http://dbpedia.org/resource/Group_representation">dbr:Group_representation</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Group_ring" href="http://dbpedia.org/resource/Group_ring">dbr:Group_ring</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Zero_ideal" href="http://dbpedia.org/resource/Zero_ideal">dbr:Zero_ideal</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Factor_group" href="http://dbpedia.org/resource/Factor_group">dbr:Factor_group</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Injective_object" href="http://dbpedia.org/resource/Injective_object">dbr:Injective_object</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Canadian_Journal_of_Mathematics" href="http://dbpedia.org/resource/Canadian_Journal_of_Mathematics">dbr:Canadian_Journal_of_Mathematics</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Canadian_Mathematical_Bulletin" href="http://dbpedia.org/resource/Canadian_Mathematical_Bulletin">dbr:Canadian_Mathematical_Bulletin</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Category_(mathematics)" href="http://dbpedia.org/resource/Category_(mathematics)">dbr:Category_(mathematics)</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Category_of_abelian_groups" href="http://dbpedia.org/resource/Category_of_abelian_groups">dbr:Category_of_abelian_groups</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Category_theory" href="http://dbpedia.org/resource/Category_theory">dbr:Category_theory</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Rational_number" href="http://dbpedia.org/resource/Rational_number">dbr:Rational_number</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Semisimple_ring" href="http://dbpedia.org/resource/Semisimple_ring">dbr:Semisimple_ring</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Sheaf_(mathematics)" href="http://dbpedia.org/resource/Sheaf_(mathematics)">dbr:Sheaf_(mathematics)</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Ext_functor" href="http://dbpedia.org/resource/Ext_functor">dbr:Ext_functor</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Completion_(ring_theory)" href="http://dbpedia.org/resource/Completion_(ring_theory)">dbr:Completion_(ring_theory)</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Quasi-Frobenius_ring" href="http://dbpedia.org/resource/Quasi-Frobenius_ring">dbr:Quasi-Frobenius_ring</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Localization_of_a_ring" href="http://dbpedia.org/resource/Localization_of_a_ring">dbr:Localization_of_a_ring</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Exact_functor" href="http://dbpedia.org/resource/Exact_functor">dbr:Exact_functor</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Exact_sequence" href="http://dbpedia.org/resource/Exact_sequence">dbr:Exact_sequence</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Finite_group" href="http://dbpedia.org/resource/Finite_group">dbr:Finite_group</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Uniform_module" href="http://dbpedia.org/resource/Uniform_module">dbr:Uniform_module</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Injective" href="http://dbpedia.org/resource/Injective">dbr:Injective</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Pacific_Journal_of_Mathematics" href="http://dbpedia.org/resource/Pacific_Journal_of_Mathematics">dbr:Pacific_Journal_of_Mathematics</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Transactions_of_the_American_Mathematical_Society" href="http://dbpedia.org/resource/Transactions_of_the_American_Mathematical_Society">dbr:Transactions_of_the_American_Mathematical_Society</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Split_exact_sequence" href="http://dbpedia.org/resource/Split_exact_sequence">dbr:Split_exact_sequence</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Duality_of_categories" href="http://dbpedia.org/resource/Duality_of_categories">dbr:Duality_of_categories</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Basis_of_a_vector_space" href="http://dbpedia.org/resource/Basis_of_a_vector_space">dbr:Basis_of_a_vector_space</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Submodule" href="http://dbpedia.org/resource/Submodule">dbr:Submodule</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Springer-Verlag" href="http://dbpedia.org/resource/Springer-Verlag">dbr:Springer-Verlag</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Divisible_module" href="http://dbpedia.org/resource/Divisible_module">dbr:Divisible_module</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Prime_spectrum" href="http://dbpedia.org/resource/Prime_spectrum">dbr:Prime_spectrum</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Pure_injective_module" href="http://dbpedia.org/resource/Pure_injective_module">dbr:Pure_injective_module</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Dimension_of_a_vector_space" href="http://dbpedia.org/resource/Dimension_of_a_vector_space">dbr:Dimension_of_a_vector_space</a></li> <li><a class="uri" rel="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/File:Injective_module.svg" href="http://dbpedia.org/resource/File:Injective_module.svg">dbr:File:Injective_module.svg</a></li> </ul></td></tr><tr class="even"><td class="col-2"><a class="uri" href="http://dbpedia.org/property/b">dbp:b</a> </td><td class="col-10 text-break"><ul> <li>A (en)</li> </ul></td></tr><tr class="odd"><td class="col-2"><a class="uri" href="http://dbpedia.org/property/p">dbp:p</a> </td><td class="col-10 text-break"><ul> <li>N (en)</li> </ul></td></tr><tr class="even"><td class="col-2"><a class="uri" href="http://dbpedia.org/property/wikiPageUsesTemplate">dbp:wikiPageUsesTemplate</a> </td><td class="col-10 text-break"><ul> <li><a class="uri" rel="dbp:wikiPageUsesTemplate" resource="http://dbpedia.org/resource/Template:Authority_control" href="http://dbpedia.org/resource/Template:Authority_control">dbt:Authority_control</a></li> <li><a class="uri" rel="dbp:wikiPageUsesTemplate" resource="http://dbpedia.org/resource/Template:Citation" href="http://dbpedia.org/resource/Template:Citation">dbt:Citation</a></li> <li><a class="uri" rel="dbp:wikiPageUsesTemplate" resource="http://dbpedia.org/resource/Template:Harv" href="http://dbpedia.org/resource/Template:Harv">dbt:Harv</a></li> <li><a class="uri" rel="dbp:wikiPageUsesTemplate" resource="http://dbpedia.org/resource/Template:Main" href="http://dbpedia.org/resource/Template:Main">dbt:Main</a></li> <li><a class="uri" rel="dbp:wikiPageUsesTemplate" resource="http://dbpedia.org/resource/Template:Reflist" href="http://dbpedia.org/resource/Template:Reflist">dbt:Reflist</a></li> <li><a class="uri" rel="dbp:wikiPageUsesTemplate" resource="http://dbpedia.org/resource/Template:Short_description" href="http://dbpedia.org/resource/Template:Short_description">dbt:Short_description</a></li> <li><a class="uri" rel="dbp:wikiPageUsesTemplate" resource="http://dbpedia.org/resource/Template:Su" href="http://dbpedia.org/resource/Template:Su">dbt:Su</a></li> </ul></td></tr><tr class="odd"><td class="col-2"><a class="uri" href="http://purl.org/dc/terms/subject">dcterms:subject</a> </td><td class="col-10 text-break"><ul> <li><a class="uri" rel="dcterms:subject" resource="http://dbpedia.org/resource/Category:Module_theory" prefix="dcterms: http://purl.org/dc/terms/" href="http://dbpedia.org/resource/Category:Module_theory">dbc:Module_theory</a></li> <li><a class="uri" rel="dcterms:subject" resource="http://dbpedia.org/resource/Category:Homological_algebra" prefix="dcterms: http://purl.org/dc/terms/" href="http://dbpedia.org/resource/Category:Homological_algebra">dbc:Homological_algebra</a></li> </ul></td></tr><tr class="even"><td class="col-2"><a class="uri" href="http://purl.org/linguistics/gold/hypernym">gold:hypernym</a> </td><td class="col-10 text-break"><ul> <li><a class="uri" rel="gold:hypernym" resource="http://dbpedia.org/resource/Q" prefix="gold: http://purl.org/linguistics/gold/" href="http://dbpedia.org/resource/Q">dbr:Q</a></li> </ul></td></tr><tr class="odd"><td class="col-2"><a class="uri" href="http://www.w3.org/1999/02/22-rdf-syntax-ns#type">rdf:type</a> </td><td class="col-10 text-break"><ul> <li><a class="uri" rel="rdf:type" resource="http://www.w3.org/2002/07/owl#Thing" href="http://www.w3.org/2002/07/owl#Thing">owl:Thing</a></li> <li><a class="uri" rel="rdf:type" resource="http://dbpedia.org/ontology/Work" href="http://dbpedia.org/ontology/Work">dbo:Work</a></li> </ul></td></tr><tr class="even"><td class="col-2"><a class="uri" href="http://www.w3.org/2000/01/rdf-schema#comment">rdfs:comment</a> </td><td class="col-10 text-break"><ul> <li style="display:none;">En matemáticas, un módulo inyectivo es un módulo Q que comparte ciertas propiedades deseables con el Z-módulo Q de todos los números racionales. Específicamente, si Q es un submódulo de algún otro módulo, entonces es un sumando directo de ese módulo; también, dado un submódulo de un módulo Y, entonces cualquier homomorfismo de módulos de este submódulo a Q se puede ampliar a un homomorfismo de todo Y a Q. Este concepto es dual al de los módulos proyectivos. (es)</li> <li style="display:none;">En mathématiques, et plus spécifiquement en algèbre homologique, un module injectif est un module Q (à gauche par exemple) sur un anneau A tel que pour tout morphisme injectif f : X → Y entre deux A-modules (à gauche) et pour tout morphisme g : X → Q, il existe un morphisme h : Y → Q tel que hf = g, c'est-à-dire tel que le diagramme suivant commute : Autrement dit : Q est injectif si pour tout module Y, tout morphisme d'un sous-module de Y vers Q s'étend à Y. (fr)</li> <li style="display:none;">In matematica, un modulo iniettivo è un modulo con la proprietà di essere un addendo diretto di ogni modulo che lo contiene: ovvero Q è iniettivo se, per ogni modulo M che lo contiene, esiste un sottomodulo N di M tale che M è la somma diretta di N e Q. Questo concetto è il duale di quello di modulo proiettivo; è stato introdotto da nel 1940. Un esempio di modulo iniettivo è lo -modulo dei numeri razionali. (it)</li> <li style="display:none;">数学において、入射加群（にゅうしゃかぐん、英: injective module）、あるいは移入加群（いにゅうかぐん）とは、関手 Hom(–, E) が完全となるような加群 E のことである。ホモロジー代数における基本的な概念のひとつ。 (ja)</li> <li style="display:none;">환론에서 단사 가군(單射加群, 영어: injective module)은 이를 포함하는 모든 가군을 직합으로 쪼갤 수 있는 가군이다. 가군의 범주에서의 단사 대상이다. (ko)</li> <li style="display:none;">Ін'єктивний модуль — один з типів модулів, що є двоїстим до проєктивного модуля і широко використовується в гомологічній алгебрі і загалом в теорії кілець. (uk)</li> <li style="display:none;">內射模（英語：injective module），在模論中，是具有與有理數（視為 -模）相似性質的模。內射模是投射模的對偶概念，由Reinhold Baer於1940年引進。 (zh)</li> <li>In mathematics, especially in the area of abstract algebra known as module theory, an injective module is a module Q that shares certain desirable properties with the Z-module Q of all rational numbers. Specifically, if Q is a submodule of some other module, then it is already a direct summand of that module; also, given a submodule of a module Y, then any module homomorphism from this submodule to Q can be extended to a homomorphism from all of Y to Q. This concept is dual to that of projective modules. Injective modules were introduced in and are discussed in some detail in the textbook . (en)</li> <li style="display:none;">Инъекти́вный мо́дуль — одно из основных понятий гомологической алгебры. Модуль над кольцом (как правило, считаемым ассоциативным с единичным элементом) называется инъективным, если для всякого гомоморфизма и мономорфизма (инъективного гомоморфизма) существует такой гомоморфизм , что , то есть данная диаграмма коммутативна: Можно указать ещё один критерий инъективности: инъективен тогда и только тогда, когда для любого мономорфизма индуцированный гомоморфизм является эпиморфизмом. Прямое произведение модулей инъективно тогда и только тогда, когда инъективен каждый сомножитель. (ru)</li> </ul></td></tr><tr class="odd"><td class="col-2"><a class="uri" href="http://www.w3.org/2000/01/rdf-schema#label">rdfs:label</a> </td><td class="col-10 text-break"><ul> <li style="display:none;">Módulo inyectivo (es)</li> <li style="display:none;">Module injectif (fr)</li> <li style="display:none;">Modulo iniettivo (it)</li> <li>Injective module (en)</li> <li style="display:none;">단사 가군 (ko)</li> <li style="display:none;">入射加群 (ja)</li> <li style="display:none;">Инъективный модуль (ru)</li> <li style="display:none;">Ін'єктивний модуль (uk)</li> <li style="display:none;">內射模 (zh)</li> </ul></td></tr><tr class="even"><td class="col-2"><a class="uri" href="http://www.w3.org/2002/07/owl#sameAs">owl:sameAs</a> </td><td class="col-10 text-break"><ul> <li><a class="uri" rel="owl:sameAs" resource="http://rdf.freebase.com/ns/m.02dtnj" href="http://rdf.freebase.com/ns/m.02dtnj">freebase:Injective module</a></li> <li><a class="uri" rel="owl:sameAs" resource="http://www.wikidata.org/entity/Q2716519" href="http://www.wikidata.org/entity/Q2716519">wikidata:Injective module</a></li> <li><a class="uri" rel="owl:sameAs" resource="http://es.dbpedia.org/resource/Módulo_inyectivo" href="http://es.dbpedia.org/resource/Módulo_inyectivo">dbpedia-es:Injective module</a></li> <li><a class="uri" rel="owl:sameAs" resource="http://fa.dbpedia.org/resource/مدول_تزریقی" href="http://fa.dbpedia.org/resource/مدول_تزریقی">dbpedia-fa:Injective module</a></li> <li><a class="uri" rel="owl:sameAs" resource="http://fr.dbpedia.org/resource/Module_injectif" href="http://fr.dbpedia.org/resource/Module_injectif">dbpedia-fr:Injective module</a></li> <li><a class="uri" rel="owl:sameAs" resource="http://he.dbpedia.org/resource/מודול_אינג'קטיבי" href="http://he.dbpedia.org/resource/מודול_אינג'קטיבי">dbpedia-he:Injective module</a></li> <li><a class="uri" rel="owl:sameAs" resource="http://it.dbpedia.org/resource/Modulo_iniettivo" href="http://it.dbpedia.org/resource/Modulo_iniettivo">dbpedia-it:Injective module</a></li> <li><a class="uri" rel="owl:sameAs" resource="http://ja.dbpedia.org/resource/入射加群" href="http://ja.dbpedia.org/resource/入射加群">dbpedia-ja:Injective module</a></li> <li><a class="uri" rel="owl:sameAs" resource="http://ko.dbpedia.org/resource/단사_가군" href="http://ko.dbpedia.org/resource/단사_가군">dbpedia-ko:Injective module</a></li> <li><a class="uri" rel="owl:sameAs" resource="http://ru.dbpedia.org/resource/Инъективный_модуль" href="http://ru.dbpedia.org/resource/Инъективный_модуль">dbpedia-ru:Injective module</a></li> <li><a class="uri" rel="owl:sameAs" resource="http://uk.dbpedia.org/resource/Ін'єктивний_модуль" href="http://uk.dbpedia.org/resource/Ін'єктивний_модуль">dbpedia-uk:Injective module</a></li> <li><a class="uri" rel="owl:sameAs" resource="http://zh.dbpedia.org/resource/內射模" href="http://zh.dbpedia.org/resource/內射模">dbpedia-zh:Injective module</a></li> <li><a class="uri" rel="owl:sameAs" resource="https://global.dbpedia.org/id/2YTw3" href="https://global.dbpedia.org/id/2YTw3">https://global.dbpedia.org/id/2YTw3</a></li> </ul></td></tr><tr class="odd"><td class="col-2"><a class="uri" href="http://www.w3.org/ns/prov#wasDerivedFrom">prov:wasDerivedFrom</a> </td><td class="col-10 text-break"><ul> <li><a class="uri" rel="prov:wasDerivedFrom" resource="http://en.wikipedia.org/wiki/Injective_module?oldid=1121784240&ns=0" href="http://en.wikipedia.org/wiki/Injective_module?oldid=1121784240&ns=0">wikipedia-en:Injective_module?oldid=1121784240&ns=0</a></li> </ul></td></tr><tr class="even"><td class="col-2"><a class="uri" href="http://xmlns.com/foaf/0.1/depiction">foaf:depiction</a> </td><td class="col-10 text-break"><ul> <li><a class="uri" rel="foaf:depiction" resource="http://commons.wikimedia.org/wiki/Special:FilePath/Injective_module.svg" href="http://commons.wikimedia.org/wiki/Special:FilePath/Injective_module.svg">wiki-commons:Special:FilePath/Injective_module.svg</a></li> </ul></td></tr><tr class="odd"><td class="col-2"><a class="uri" href="http://xmlns.com/foaf/0.1/isPrimaryTopicOf">foaf:isPrimaryTopicOf</a> </td><td class="col-10 text-break"><ul> <li><a class="uri" rel="foaf:isPrimaryTopicOf" resource="http://en.wikipedia.org/wiki/Injective_module" href="http://en.wikipedia.org/wiki/Injective_module">wikipedia-en:Injective_module</a></li> </ul></td></tr><tr class="even"><td class="col-2">is <a class="uri" href="http://dbpedia.org/ontology/knownFor">dbo:knownFor</a> of</td><td class="col-10 text-break"><ul> <li><a class="uri" rev="dbo:knownFor" resource="http://dbpedia.org/resource/Reinhold_Baer" href="http://dbpedia.org/resource/Reinhold_Baer">dbr:Reinhold_Baer</a></li> </ul></td></tr><tr class="odd"><td class="col-2">is <a class="uri" href="http://dbpedia.org/ontology/wikiPageRedirects">dbo:wikiPageRedirects</a> of</td><td class="col-10 text-break"><ul> <li><a class="uri" rev="dbo:wikiPageRedirects" resource="http://dbpedia.org/resource/Injective_dimension" href="http://dbpedia.org/resource/Injective_dimension">dbr:Injective_dimension</a></li> <li><a class="uri" rev="dbo:wikiPageRedirects" resource="http://dbpedia.org/resource/Injective_test_lemma" href="http://dbpedia.org/resource/Injective_test_lemma">dbr:Injective_test_lemma</a></li> <li><a class="uri" rev="dbo:wikiPageRedirects" resource="http://dbpedia.org/resource/Baer's_criterion" href="http://dbpedia.org/resource/Baer's_criterion">dbr:Baer's_criterion</a></li> <li><a class="uri" rev="dbo:wikiPageRedirects" resource="http://dbpedia.org/resource/Self-injective_ring" href="http://dbpedia.org/resource/Self-injective_ring">dbr:Self-injective_ring</a></li> </ul></td></tr><tr class="even"><td class="col-2">is <a class="uri" href="http://dbpedia.org/ontology/wikiPageWikiLink">dbo:wikiPageWikiLink</a> of</td><td class="col-10 text-break"><ul> <li><a class="uri" rev="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Endomorphism_ring" href="http://dbpedia.org/resource/Endomorphism_ring">dbr:Endomorphism_ring</a></li> <li><a class="uri" rev="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/List_of_abstract_algebra_topics" href="http://dbpedia.org/resource/List_of_abstract_algebra_topics">dbr:List_of_abstract_algebra_topics</a></li> <li><a class="uri" rev="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/List_of_commutative_algebra_topics" href="http://dbpedia.org/resource/List_of_commutative_algebra_topics">dbr:List_of_commutative_algebra_topics</a></li> <li><a class="uri" rev="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Module_(mathematics)" href="http://dbpedia.org/resource/Module_(mathematics)">dbr:Module_(mathematics)</a></li> <li><a class="uri" rev="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Primitive_ring" href="http://dbpedia.org/resource/Primitive_ring">dbr:Primitive_ring</a></li> <li><a class="uri" rev="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Bijection,_injection_and_surjection" href="http://dbpedia.org/resource/Bijection,_injection_and_surjection">dbr:Bijection,_injection_and_surjection</a></li> <li><a class="uri" rev="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Algebraically_compact_module" href="http://dbpedia.org/resource/Algebraically_compact_module">dbr:Algebraically_compact_module</a></li> <li><a class="uri" rev="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Reinhold_Baer" href="http://dbpedia.org/resource/Reinhold_Baer">dbr:Reinhold_Baer</a></li> <li><a class="uri" rev="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Character_module" href="http://dbpedia.org/resource/Character_module">dbr:Character_module</a></li> <li><a class="uri" rev="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Dedekind_domain" href="http://dbpedia.org/resource/Dedekind_domain">dbr:Dedekind_domain</a></li> <li><a class="uri" rev="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Injective_hull" href="http://dbpedia.org/resource/Injective_hull">dbr:Injective_hull</a></li> <li><a class="uri" rev="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Lifting_property" href="http://dbpedia.org/resource/Lifting_property">dbr:Lifting_property</a></li> <li><a class="uri" rev="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/List_of_homological_algebra_topics" href="http://dbpedia.org/resource/List_of_homological_algebra_topics">dbr:List_of_homological_algebra_topics</a></li> <li><a class="uri" rev="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/List_of_lemmas" href="http://dbpedia.org/resource/List_of_lemmas">dbr:List_of_lemmas</a></li> <li><a class="uri" rev="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Timeline_of_category_theory_and_related_mathematics" href="http://dbpedia.org/resource/Timeline_of_category_theory_and_related_mathematics">dbr:Timeline_of_category_theory_and_related_mathematics</a></li> <li><a class="uri" rev="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Essential_extension" href="http://dbpedia.org/resource/Essential_extension">dbr:Essential_extension</a></li> <li><a class="uri" rev="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Noetherian_ring" href="http://dbpedia.org/resource/Noetherian_ring">dbr:Noetherian_ring</a></li> <li><a class="uri" rev="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Serial_module" href="http://dbpedia.org/resource/Serial_module">dbr:Serial_module</a></li> <li><a class="uri" rev="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Glossary_of_commutative_algebra" href="http://dbpedia.org/resource/Glossary_of_commutative_algebra">dbr:Glossary_of_commutative_algebra</a></li> <li><a class="uri" rev="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Glossary_of_module_theory" href="http://dbpedia.org/resource/Glossary_of_module_theory">dbr:Glossary_of_module_theory</a></li> <li><a class="uri" rev="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Glossary_of_ring_theory" href="http://dbpedia.org/resource/Glossary_of_ring_theory">dbr:Glossary_of_ring_theory</a></li> <li><a class="uri" rev="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Morita_equivalence" href="http://dbpedia.org/resource/Morita_equivalence">dbr:Morita_equivalence</a></li> <li><a class="uri" rev="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Bass_number" href="http://dbpedia.org/resource/Bass_number">dbr:Bass_number</a></li> <li><a class="uri" rev="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Frobenius_algebra" href="http://dbpedia.org/resource/Frobenius_algebra">dbr:Frobenius_algebra</a></li> <li><a class="uri" rev="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Idempotent_(ring_theory)" href="http://dbpedia.org/resource/Idempotent_(ring_theory)">dbr:Idempotent_(ring_theory)</a></li> <li><a class="uri" rev="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Triangulated_category" href="http://dbpedia.org/resource/Triangulated_category">dbr:Triangulated_category</a></li> <li><a class="uri" rev="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Divisible_group" href="http://dbpedia.org/resource/Divisible_group">dbr:Divisible_group</a></li> <li><a class="uri" rev="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Duality_(mathematics)" href="http://dbpedia.org/resource/Duality_(mathematics)">dbr:Duality_(mathematics)</a></li> <li><a class="uri" rev="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Projective_module" href="http://dbpedia.org/resource/Projective_module">dbr:Projective_module</a></li> <li><a class="uri" rev="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Projective_object" href="http://dbpedia.org/resource/Projective_object">dbr:Projective_object</a></li> <li><a class="uri" rev="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Resolution_(algebra)" href="http://dbpedia.org/resource/Resolution_(algebra)">dbr:Resolution_(algebra)</a></li> <li><a class="uri" rev="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Baer_ring" href="http://dbpedia.org/resource/Baer_ring">dbr:Baer_ring</a></li> <li><a class="uri" rev="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Associated_prime" href="http://dbpedia.org/resource/Associated_prime">dbr:Associated_prime</a></li> <li><a class="uri" rev="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Abelian_group" href="http://dbpedia.org/resource/Abelian_group">dbr:Abelian_group</a></li> <li><a class="uri" rev="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Joachim_Lambek" href="http://dbpedia.org/resource/Joachim_Lambek">dbr:Joachim_Lambek</a></li> <li><a class="uri" rev="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Coherent_ring" href="http://dbpedia.org/resource/Coherent_ring">dbr:Coherent_ring</a></li> <li><a class="uri" rev="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Eben_Matlis" href="http://dbpedia.org/resource/Eben_Matlis">dbr:Eben_Matlis</a></li> <li><a class="uri" rev="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Homotopy_theory" href="http://dbpedia.org/resource/Homotopy_theory">dbr:Homotopy_theory</a></li> <li><a class="uri" rev="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Axiom_of_choice" href="http://dbpedia.org/resource/Axiom_of_choice">dbr:Axiom_of_choice</a></li> <li><a class="uri" rev="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Injective_object" href="http://dbpedia.org/resource/Injective_object">dbr:Injective_object</a></li> <li><a class="uri" rev="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Category_of_abelian_groups" href="http://dbpedia.org/resource/Category_of_abelian_groups">dbr:Category_of_abelian_groups</a></li> <li><a class="uri" rev="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Slender_group" href="http://dbpedia.org/resource/Slender_group">dbr:Slender_group</a></li> <li><a class="uri" rev="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/V-ring_(ring_theory)" href="http://dbpedia.org/resource/V-ring_(ring_theory)">dbr:V-ring_(ring_theory)</a></li> <li><a class="uri" rev="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Ext_functor" href="http://dbpedia.org/resource/Ext_functor">dbr:Ext_functor</a></li> <li><a class="uri" rev="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Quasi-Frobenius_ring" href="http://dbpedia.org/resource/Quasi-Frobenius_ring">dbr:Quasi-Frobenius_ring</a></li> <li><a class="uri" rev="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Singular_submodule" href="http://dbpedia.org/resource/Singular_submodule">dbr:Singular_submodule</a></li> <li><a class="uri" rev="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Exact_functor" href="http://dbpedia.org/resource/Exact_functor">dbr:Exact_functor</a></li> <li><a class="uri" rev="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Stable_module_category" href="http://dbpedia.org/resource/Stable_module_category">dbr:Stable_module_category</a></li> <li><a class="uri" rev="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Uniform_module" href="http://dbpedia.org/resource/Uniform_module">dbr:Uniform_module</a></li> <li><a class="uri" rev="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Semisimple_module" href="http://dbpedia.org/resource/Semisimple_module">dbr:Semisimple_module</a></li> <li><a class="uri" rev="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Perfect_ring" href="http://dbpedia.org/resource/Perfect_ring">dbr:Perfect_ring</a></li> <li><a class="uri" rev="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Outline_of_algebraic_structures" href="http://dbpedia.org/resource/Outline_of_algebraic_structures">dbr:Outline_of_algebraic_structures</a></li> <li><a class="uri" rev="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Injective_dimension" href="http://dbpedia.org/resource/Injective_dimension">dbr:Injective_dimension</a></li> <li><a class="uri" rev="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Injective_test_lemma" href="http://dbpedia.org/resource/Injective_test_lemma">dbr:Injective_test_lemma</a></li> <li><a class="uri" rev="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Baer's_criterion" href="http://dbpedia.org/resource/Baer's_criterion">dbr:Baer's_criterion</a></li> <li><a class="uri" rev="dbo:wikiPageWikiLink" resource="http://dbpedia.org/resource/Self-injective_ring" href="http://dbpedia.org/resource/Self-injective_ring">dbr:Self-injective_ring</a></li> </ul></td></tr><tr class="odd"><td class="col-2">is <a class="uri" href="http://dbpedia.org/property/knownFor">dbp:knownFor</a> of</td><td class="col-10 text-break"><ul> <li><a class="uri" rev="dbp:knownFor" resource="http://dbpedia.org/resource/Reinhold_Baer" href="http://dbpedia.org/resource/Reinhold_Baer">dbr:Reinhold_Baer</a></li> </ul></td></tr><tr class="even"><td class="col-2">is <a class="uri" href="http://xmlns.com/foaf/0.1/primaryTopic">foaf:primaryTopic</a> of</td><td class="col-10 text-break"><ul> <li><a class="uri" rev="foaf:primaryTopic" resource="http://en.wikipedia.org/wiki/Injective_module" href="http://en.wikipedia.org/wiki/Injective_module">wikipedia-en:Injective_module</a></li> </ul></td></tr> </tbody> </table> </div> </div> </div> </section>   <section> <div class="container-xl"> <div class="text-center p-4 bg-light"> <a href="https://virtuoso.openlinksw.com/" title="OpenLink Virtuoso"><img class="powered_by" src="/statics/images/virt_power_no_border.png" alt="Powered by OpenLink Virtuoso"/></a>    <a href="http://linkeddata.org/"><img alt="This material is Open Knowledge" src="/statics/images/LoDLogo.gif"/></a>     <a href="http://dbpedia.org/sparql"><img alt="W3C Semantic Web Technology" src="/statics/images/sw-sparql-blue.png"/></a>     <a href="https://opendefinition.org/"><img alt="This material is Open Knowledge" src="/statics/images/od_80x15_red_green.png"/></a>    <a href="https://validator.w3.org/check?uri=referer"> <img src="https://www.w3.org/Icons/valid-xhtml-rdfa" alt="Valid XHTML + RDFa" /> </a> This content was extracted from <a href="http://en.wikipedia.org/wiki/Injective_module">Wikipedia</a> and is licensed under the <a href="http://creativecommons.org/licenses/by-sa/3.0/">Creative Commons Attribution-ShareAlike 3.0 Unported License</a> </div> </div> </section>   <script src="https://cdnjs.cloudflare.com/ajax/libs/bootstrap/5.2.1/js/bootstrap.bundle.min.js" integrity="sha512-1TK4hjCY5+E9H3r5+05bEGbKGyK506WaDPfPe1s/ihwRjr6OtL43zJLzOFQ+/zciONEd+sp7LwrfOCnyukPSsg==" crossorigin="anonymous"> </script> </body> </html>