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Available in 16 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-16" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">16 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ba mw-list-item"><a href="https://ba.wikipedia.org/wiki/%D0%9C%D0%B0%D0%BB%D1%8C%D1%86%D0%B5%D0%B2_%D0%90%D0%BD%D0%B0%D1%82%D0%BE%D0%BB%D0%B8%D0%B9_%D0%98%D0%B2%D0%B0%D0%BD%D0%BE%D0%B2%D0%B8%D1%87" title="Мальцев Анатолий Иванович – Bashkir" lang="ba" hreflang="ba" data-title="Мальцев Анатолий Иванович" data-language-autonym="Башҡортса" data-language-local-name="Bashkir" class="interlanguage-link-target"><span>Башҡортса</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Anatoli_Maltsev" title="Anatoli Maltsev – Catalan" lang="ca" hreflang="ca" data-title="Anatoli Maltsev" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Anatoli_Iwanowitsch_Malzew" title="Anatoli Iwanowitsch Malzew – German" lang="de" hreflang="de" data-title="Anatoli Iwanowitsch Malzew" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Anatoli_M%C3%A1ltsev" title="Anatoli Máltsev – Spanish" lang="es" hreflang="es" data-title="Anatoli Máltsev" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Anatoli_Maltsev" title="Anatoli Maltsev – French" lang="fr" hreflang="fr" data-title="Anatoli Maltsev" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%95%84%EB%82%98%ED%86%A8%EB%A6%AC_%EB%A7%90%EC%B2%B4%ED%94%84" title="아나톨리 말체프 – Korean" lang="ko" hreflang="ko" data-title="아나톨리 말체프" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%B1%D5%B6%D5%A1%D5%BF%D5%B8%D5%AC%D5%AB_%D5%84%D5%A1%D5%AC%D6%81%D6%87" title="Անատոլի Մալցև – Armenian" lang="hy" hreflang="hy" data-title="Անատոլի Մալցև" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/Anatoly_Maltsev" title="Anatoly Maltsev – Haitian Creole" lang="ht" hreflang="ht" data-title="Anatoly Maltsev" data-language-autonym="Kreyòl ayisyen" data-language-local-name="Haitian Creole" class="interlanguage-link-target"><span>Kreyòl ayisyen</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%85%E0%A4%A8%E0%A4%BE%E0%A4%A4%E0%A5%8B%E0%A4%B2%E0%A5%80_%E0%A4%AE%E0%A4%BE%E0%A4%B2%E0%A5%8D%E0%A4%A4%E0%A5%8D%E0%A4%B8%E0%A5%87%E0%A4%B5" title="अनातोली माल्त्सेव – Marathi" lang="mr" hreflang="mr" data-title="अनातोली माल्त्सेव" data-language-autonym="मराठी" data-language-local-name="Marathi" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-arz mw-list-item"><a href="https://arz.wikipedia.org/wiki/%D8%A7%D9%86%D8%A7%D8%AA%D9%88%D9%84%D9%89_%D9%85%D8%A7%D9%84%D8%AA%D8%B3%D9%8A%DA%A4" title="اناتولى مالتسيڤ – Egyptian Arabic" lang="arz" hreflang="arz" data-title="اناتولى مالتسيڤ" data-language-autonym="مصرى" data-language-local-name="Egyptian Arabic" class="interlanguage-link-target"><span>مصرى</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Anatolij_Malcew" title="Anatolij Malcew – Polish" lang="pl" hreflang="pl" data-title="Anatolij Malcew" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Anatoly_Maltsev" title="Anatoly Maltsev – Portuguese" lang="pt" hreflang="pt" data-title="Anatoly Maltsev" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Anatoli_Mal%C8%9Bev" title="Anatoli Malțev – Romanian" lang="ro" hreflang="ro" data-title="Anatoli Malțev" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9C%D0%B0%D0%BB%D1%8C%D1%86%D0%B5%D0%B2,_%D0%90%D0%BD%D0%B0%D1%82%D0%BE%D0%BB%D0%B8%D0%B9_%D0%98%D0%B2%D0%B0%D0%BD%D0%BE%D0%B2%D0%B8%D1%87" title="Мальцев, Анатолий Иванович – Russian" lang="ru" hreflang="ru" data-title="Мальцев, Анатолий Иванович" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/%D0%90%D0%BD%D0%B0%D1%82%D0%BE%D0%BB%D0%B8%D0%B9_%D0%9C%D0%B0%D0%BB%D1%8C%D1%86%D0%B5%D0%B2" title="Анатолий Мальцев – Tatar" lang="tt" hreflang="tt" data-title="Анатолий Мальцев" data-language-autonym="Татарча / tatarça" data-language-local-name="Tatar" class="interlanguage-link-target"><span>Татарча / tatarça</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%9C%D0%B0%D0%BB%D1%8C%D1%86%D0%B5%D0%B2_%D0%90%D0%BD%D0%B0%D1%82%D0%BE%D0%BB%D1%96%D0%B9_%D0%86%D0%B2%D0%B0%D0%BD%D0%BE%D0%B2%D0%B8%D1%87" title="Мальцев Анатолій Іванович – Ukrainian" lang="uk" hreflang="uk" data-title="Мальцев Анатолій Іванович" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a 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hosted by Wikidata [g]" accesskey="g"><span>Wikidata item</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> </div> </div> </div> <div class="vector-column-end"> <div class="vector-sticky-pinned-container"> <nav class="vector-page-tools-landmark" aria-label="Page tools"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Appearance"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Appearance</div> <button 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src="//upload.wikimedia.org/wikipedia/commons/thumb/0/02/Cherbuzinskoye_cemetery3032.jpg/220px-Cherbuzinskoye_cemetery3032.jpg" decoding="async" width="220" height="132" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/02/Cherbuzinskoye_cemetery3032.jpg/330px-Cherbuzinskoye_cemetery3032.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/02/Cherbuzinskoye_cemetery3032.jpg/440px-Cherbuzinskoye_cemetery3032.jpg 2x" data-file-width="3264" data-file-height="1952" /></a><figcaption></figcaption></figure> <p><b>Anatoly Ivanovich Maltsev</b> (also: <b>Malcev</b>, <b>Mal'cev</b>; <a href="/wiki/Russian_language" title="Russian language">Russian</a>: Анато́лий Ива́нович Ма́льцев; 27 November <a href="/wiki/New_Style" class="mw-redirect" title="New Style">N.S.</a>/14 November <a href="/wiki/Old_Style" class="mw-redirect" title="Old Style">O.S.</a> 1909, <a href="/wiki/Moscow_Governorate" title="Moscow Governorate">Moscow Governorate</a> – 7 June 1967, <a href="/wiki/Novosibirsk" title="Novosibirsk">Novosibirsk</a>) was born in <a href="/wiki/Misheronsky" title="Misheronsky">Misheronsky</a>, near <a href="/wiki/Moscow" title="Moscow">Moscow</a>, and died in <a href="/wiki/Novosibirsk" title="Novosibirsk">Novosibirsk</a>, <a href="/wiki/Soviet_Union" title="Soviet Union">USSR</a>. He was a <a href="/wiki/Mathematician" title="Mathematician">mathematician</a> noted for his work on the <a href="/wiki/Decidability_(logic)" title="Decidability (logic)">decidability</a> of various <a href="/wiki/Algebraic_group" title="Algebraic group">algebraic groups</a>. <a href="/wiki/Malcev_algebra" title="Malcev algebra">Malcev algebras</a> (generalisations of <a href="/wiki/Lie_algebra" title="Lie algebra">Lie algebras</a>), as well as <a href="/wiki/Malcev_Lie_algebra" title="Malcev Lie algebra">Malcev Lie algebras</a> are named after him. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Biography">Biography</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Anatoly_Maltsev&action=edit&section=1" title="Edit section: Biography"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>At school, Maltsev demonstrated an aptitude for mathematics, and when he left school in 1927, he went to <a href="/wiki/Moscow_State_University" title="Moscow State University">Moscow State University</a> to study <a href="/wiki/Mathematics" title="Mathematics">Mathematics</a>. While he was there, he started teaching in a secondary school in Moscow. After graduating in 1931, he continued his teaching career and in 1932 was appointed as an assistant at the <a href="/wiki/Ivanovo_State_University" title="Ivanovo State University">Ivanovo Pedagogical Institute</a> located in <a href="/wiki/Ivanovo" title="Ivanovo">Ivanovo</a>, near Moscow. </p><p>Whilst teaching at Ivanovo, Maltsev made frequent trips to Moscow to discuss his research with <a href="/wiki/Kolmogorov" class="mw-redirect" title="Kolmogorov">Kolmogorov</a>. Maltsev's first publications were on <a href="/wiki/Logic" title="Logic">logic</a> and <a href="/wiki/Model_theory" title="Model theory">model theory</a>. Kolmogorov soon invited him to join his graduate programme at Moscow State University, and, maintaining his post at Ivanovo, Maltsev effectively became Kolmogorov's student. </p><p>In 1937, Maltsev published a paper on the <a href="/wiki/Embedding" title="Embedding">embedding</a> of a <a href="/wiki/Ring_(mathematics)" title="Ring (mathematics)">ring</a> in a <a href="/wiki/Field_(mathematics)" title="Field (mathematics)">field</a>. Two years later, he published a second paper where he gave necessary and sufficient conditions for a <a href="/wiki/Semigroup" title="Semigroup">semigroup</a> to be embeddable in a <a href="/wiki/Group_(mathematics)" title="Group (mathematics)">group</a>. </p><p>Between 1939 and 1941, he studied for his doctorate at the <a href="/wiki/Steklov_Institute" class="mw-redirect" title="Steklov Institute">Steklov Institute</a> of the <a href="/wiki/USSR_Academy_of_Sciences" class="mw-redirect" title="USSR Academy of Sciences">USSR Academy of Sciences</a>, with a dissertation on the <i>Structure of isomorphic representable infinite algebras and groups</i>. </p><p>In 1944, Maltsev became a professor at the <a href="/w/index.php?title=Ivanovo_Pedagogical&action=edit&redlink=1" class="new" title="Ivanovo Pedagogical (page does not exist)">Ivanovo Pedagogical</a> Institute where he continued to work on <a href="/wiki/Group_theory" title="Group theory">group theory</a> and <a href="/wiki/Linear_group" title="Linear group">linear groups</a> in particular. He also studied <a href="/wiki/Lie_group" title="Lie group">Lie groups</a> and <a href="/wiki/Topological_algebra" title="Topological algebra">topological algebras</a>. He generalized the <a href="/wiki/Lie_group%E2%80%93Lie_algebra_correspondence" title="Lie group–Lie algebra correspondence">Lie group–Lie algebra correspondence</a>;<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> his generalization is now known as the Mal'cev correspondence.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p> <style data-mw-deduplicate="TemplateStyles:r1244412712">.mw-parser-output .templatequote{overflow:hidden;margin:1em 0;padding:0 32px}.mw-parser-output .templatequotecite{line-height:1.5em;text-align:left;margin-top:0}@media(min-width:500px){.mw-parser-output .templatequotecite{padding-left:1.6em}}</style><blockquote class="templatequote"><p>Malcev<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> proved that there is a <a href="/wiki/Category_(mathematics)" title="Category (mathematics)">category</a> isomorphism between the category of <a href="/wiki/Torsion-free_group" class="mw-redirect" title="Torsion-free group">torsion-free</a> radicable <a href="/wiki/Nilpotent_group" title="Nilpotent group">nilpotent groups</a> of finite rank and the category of nilpotent finite-dimensional rational Lie algebras. One can view this isomorphism as being given by the <a href="/wiki/Baker%E2%80%93Campbell%E2%80%93Hausdorff_formula" title="Baker–Campbell–Hausdorff formula">Campbell–Baker–Hausdorff formula</a>. This point of view is carried further by <a href="/wiki/Michel_Lazard" title="Michel Lazard">Lazard</a><sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> and Stewart.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup></p></blockquote> <p>In 1958, Maltsev became an Academician of the <a href="/wiki/Soviet_Academy_of_Sciences" class="mw-redirect" title="Soviet Academy of Sciences">Soviet Academy of Sciences</a>. In 1960, he was appointed to a chair in mathematics at the Mathematics Institute at Novosibirsk and chaired the Algebra and Logic Department of <a href="/wiki/Novosibirsk_State_University" title="Novosibirsk State University">Novosibirsk State University</a>. He founded the Siberian section of the Mathematics Institute of the Academy of Sciences, the Siberian Mathematical Society and the journal <i><a href="/wiki/Algebra_i_Logika" title="Algebra i Logika">Algebra i Logika</a></i>. Maltsev also founded the "Algebra and Logic Seminar" attended by his students <a href="/w/index.php?title=Igor_Lavrov_(mathematician)&action=edit&redlink=1" class="new" title="Igor Lavrov (mathematician) (page does not exist)">Igor Lavrov</a>, <a href="/wiki/Larisa_Maksimova" title="Larisa Maksimova">Larisa Maksimova</a>, <a href="/w/index.php?title=Dmitry_Smirnov_(mathematician)&action=edit&redlink=1" class="new" title="Dmitry Smirnov (mathematician) (page does not exist)">Dmitry Smirnov</a>, <a href="/w/index.php?title=Mikhail_Taitslin&action=edit&redlink=1" class="new" title="Mikhail Taitslin (page does not exist)">Mikhail Taitslin</a>, and A. Vinogradov, as well as by <a href="/wiki/Yuri_Ershov" class="mw-redirect" title="Yuri Ershov">Yuri Ershov</a> and others. This seminar, in essence, started a new and extremely fruitful school in <a href="/wiki/Model_theory" title="Model theory">model theory</a> and <a href="/w/index.php?title=Decidability_of_elementary_theories&action=edit&redlink=1" class="new" title="Decidability of elementary theories (page does not exist)">decidability of elementary theories</a>. </p><p>During the early 1960s, Maltsev worked on problems of <a href="/wiki/Decidability_(logic)" title="Decidability (logic)">decidability</a> of <a href="/wiki/First-order_theory" class="mw-redirect" title="First-order theory">elementary theories</a> of various algebraic structures. He showed the undecidability of the elementary theory of <a href="/wiki/Finite_group" title="Finite group">finite groups</a>, of free <a href="/wiki/Nilpotent_group" title="Nilpotent group">nilpotent groups</a>, of free <a href="/wiki/Solvable_group" title="Solvable group">soluble groups</a> and many others. He also proved that the class of locally free algebras has a decidable theory. </p><p>Maltsev received many honours, including the <a href="/wiki/State_Stalin_Prize" class="mw-redirect" title="State Stalin Prize">Stalin Prize</a> in 1946 and <a href="/wiki/Lenin_Prize" title="Lenin Prize">Lenin Prize</a> in 1964. In 1962 he founded the mathematical journal <i><a href="/wiki/Algebra_i_Logika" title="Algebra i Logika">Algebra i Logika</a></i>. </p> <div class="mw-heading mw-heading2"><h2 id="Selected_publications">Selected publications</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Anatoly_Maltsev&action=edit&section=2" title="Edit section: Selected publications"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><i>Algebraic Systems</i> by A.I. Mal'cev, Springer-Verlag, 1973, <style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-387-05792-7" title="Special:BookSources/0-387-05792-7">0-387-05792-7</a></li> <li><i>The metamathematics of algebraic systems, collected papers:1936-1967</i> by A.I. Malcev, Amsterdam, North-Holland Pub. Co., 1971, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-7204-2266-3" title="Special:BookSources/0-7204-2266-3">0-7204-2266-3</a> (xvii+494 p.; trans., ed. and provided with additional notes by Benjamin Franklin Wells, III)</li> <li><i>Algorithms and recursive functions</i> by A. I. Malcev, Groningen, Wolters-Noordhoff Pub. Co. 1970<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup></li> <li><i>Foundations of linear algebra</i> by A. I. Malcev, San Francisco, W.H. Freeman, 1963 (xi+304 p. illus.; trans. by Thomas Craig Brown; ed. by J. B. Roberts)</li></ul> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Anatoly_Maltsev&action=edit&section=3" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Hahn_series" title="Hahn series">Hahn–Mal'cev–Neumann series</a></li> <li><a href="/wiki/Malcev_algebra" title="Malcev algebra">Malcev algebra</a></li> <li><a href="/wiki/Mal%27cev%27s_criterion" title="Mal'cev's criterion">Mal'cev's criterion</a></li> <li><a href="/wiki/Malcev_Lie_algebra" title="Malcev Lie algebra">Malcev Lie algebra</a></li> <li><a href="/wiki/Malcev-admissible_algebra" title="Malcev-admissible algebra">Malcev-admissible algebra</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Anatoly_Maltsev&action=edit&section=4" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMostowski,_Andrzej1969" class="citation journal cs1"><a href="/wiki/Andrzej_Mostowski" title="Andrzej Mostowski">Mostowski, Andrzej</a> (1969). <a rel="nofollow" class="external text" href="http://projecteuclid.org/euclid.jsl/1183736792">"Review: <i>Model Correspondences</i> by A.I. Mal'cev"</a>. <i><a href="/wiki/Journal_of_Symbolic_Logic" title="Journal of Symbolic Logic">Journal of Symbolic Logic</a></i>. <b>34</b> (2): 299–300. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.2307%2F2271119">10.2307/2271119</a>. <a href="/wiki/JSTOR_(identifier)" class="mw-redirect" title="JSTOR (identifier)">JSTOR</a> <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/2271119">2271119</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:121934791">121934791</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Symbolic+Logic&rft.atitle=Review%3A+Model+Correspondences+by+A.I.+Mal%27cev&rft.volume=34&rft.issue=2&rft.pages=299-300&rft.date=1969&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A121934791%23id-name%3DS2CID&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F2271119%23id-name%3DJSTOR&rft_id=info%3Adoi%2F10.2307%2F2271119&rft.au=Mostowski%2C+Andrzej&rft_id=http%3A%2F%2Fprojecteuclid.org%2Feuclid.jsl%2F1183736792&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAnatoly+Maltsev" class="Z3988"></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFStewart,_Ian1977" class="citation journal cs1"><a href="/wiki/Ian_Stewart_(mathematician)" title="Ian Stewart (mathematician)">Stewart, Ian</a> (1977). <a rel="nofollow" class="external text" href="https://eudml.org/doc/215071">"Adjoint groups and the Mal'cev correspondence (a tale of four functors)"</a>. <i><a href="/wiki/Fundamenta_Mathematicae" title="Fundamenta Mathematicae">Fundamenta Mathematicae</a></i>. <b>97</b> (2): 71–77. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.4064%2Ffm-97-2-71-77">10.4064/fm-97-2-71-77</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Fundamenta+Mathematicae&rft.atitle=Adjoint+groups+and+the+Mal%27cev+correspondence+%28a+tale+of+four+functors%29&rft.volume=97&rft.issue=2&rft.pages=71-77&rft.date=1977&rft_id=info%3Adoi%2F10.4064%2Ffm-97-2-71-77&rft.au=Stewart%2C+Ian&rft_id=https%3A%2F%2Feudml.org%2Fdoc%2F215071&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAnatoly+Maltsev" class="Z3988"></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFVidela1990" class="citation journal cs1">Videla, Carlos R. (1990). <a rel="nofollow" class="external text" href="https://doi.org/10.1090%2FS0002-9939-1990-1014647-9">"On the Mal′cev correspondence"</a>. <i><a href="/wiki/Proceedings_of_the_American_Mathematical_Society" title="Proceedings of the American Mathematical Society">Proceedings of the American Mathematical Society</a></i>. <b>109</b> (2): 493–502. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1090%2FS0002-9939-1990-1014647-9">10.1090/S0002-9939-1990-1014647-9</a></span>. <a href="/wiki/JSTOR_(identifier)" class="mw-redirect" title="JSTOR (identifier)">JSTOR</a> <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/2048013">2048013</a>. <a href="/wiki/MR_(identifier)" class="mw-redirect" title="MR (identifier)">MR</a> <a rel="nofollow" class="external text" href="https://mathscinet.ams.org/mathscinet-getitem?mr=1014647">1014647</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Proceedings+of+the+American+Mathematical+Society&rft.atitle=On+the+Mal%E2%80%B2cev+correspondence&rft.volume=109&rft.issue=2&rft.pages=493-502&rft.date=1990&rft_id=https%3A%2F%2Fmathscinet.ams.org%2Fmathscinet-getitem%3Fmr%3D1014647%23id-name%3DMR&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F2048013%23id-name%3DJSTOR&rft_id=info%3Adoi%2F10.1090%2FS0002-9939-1990-1014647-9&rft.aulast=Videla&rft.aufirst=Carlos+R.&rft_id=https%3A%2F%2Fdoi.org%2F10.1090%252FS0002-9939-1990-1014647-9&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAnatoly+Maltsev" class="Z3988"></span></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMal'cev1949" class="citation journal cs1">Mal'cev, A. I. (1949). <a rel="nofollow" class="external text" href="https://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=im&paperid=3184&option_lang=eng">"Nilpotent torsion-free groups"</a>. <i>Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya</i>. <b>13</b>: 201–212. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0373-2436">0373-2436</a>. <a href="/wiki/MR_(identifier)" class="mw-redirect" title="MR (identifier)">MR</a> <a rel="nofollow" class="external text" href="https://mathscinet.ams.org/mathscinet-getitem?mr=0028843">0028843</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Izvestiya+Akademii+Nauk+SSSR.+Seriya+Matematicheskaya&rft.atitle=Nilpotent+torsion-free+groups&rft.volume=13&rft.pages=201-212&rft.date=1949&rft.issn=0373-2436&rft_id=https%3A%2F%2Fmathscinet.ams.org%2Fmathscinet-getitem%3Fmr%3D0028843%23id-name%3DMR&rft.aulast=Mal%27cev&rft.aufirst=A.+I.&rft_id=http%3A%2F%2Fwww.mathnet.ru%2Fphp%2Farchive.phtml%3Fwshow%3Dpaper%26jrnid%3Dim%26paperid%3D3184%26option_lang%3Deng&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAnatoly+Maltsev" class="Z3988"></span></span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLazard,_Michel1954" class="citation journal cs1"><a href="/wiki/Michel_Lazard" title="Michel Lazard">Lazard, Michel</a> (1954). <a rel="nofollow" class="external text" href="https://eudml.org/doc/81690">"Sur les groupes nilpotents et les anneaux de Lie"</a>. <i><a href="/wiki/Annales_Scientifiques_de_l%27%C3%89cole_Normale_Sup%C3%A9rieure" title="Annales Scientifiques de l'École Normale Supérieure">Annales Scientifiques de l'École Normale Supérieure</a></i>. <b>71</b> (2): 101–190. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.24033%2Fasens.1021">10.24033/asens.1021</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Annales+Scientifiques+de+l%27%C3%89cole+Normale+Sup%C3%A9rieure&rft.atitle=Sur+les+groupes+nilpotents+et+les+anneaux+de+Lie&rft.volume=71&rft.issue=2&rft.pages=101-190&rft.date=1954&rft_id=info%3Adoi%2F10.24033%2Fasens.1021&rft.au=Lazard%2C+Michel&rft_id=https%3A%2F%2Feudml.org%2Fdoc%2F81690&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAnatoly+Maltsev" class="Z3988"></span></span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWarfield,_Robert_B.1976" class="citation book cs1">Warfield, Robert B. (1976). "The Malcev correspondence". <span class="id-lock-limited" title="Free access subject to limited trial, subscription normally required"><a rel="nofollow" class="external text" href="https://archive.org/details/nilpotentgroups00warf_142"><i>Nilpotent Groups</i></a></span>. Lecture Notes in Mathematics, Volume 513. Vol. 513. pp. <a rel="nofollow" class="external text" href="https://archive.org/details/nilpotentgroups00warf_142/page/n110">104</a>–111. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2FBFb0080164">10.1007/BFb0080164</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-540-07683-4" title="Special:BookSources/978-3-540-07683-4"><bdi>978-3-540-07683-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=The+Malcev+correspondence&rft.btitle=Nilpotent+Groups&rft.series=Lecture+Notes+in+Mathematics%2C+Volume+513&rft.pages=104-111&rft.date=1976&rft_id=info%3Adoi%2F10.1007%2FBFb0080164&rft.isbn=978-3-540-07683-4&rft.au=Warfield%2C+Robert+B.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fnilpotentgroups00warf_142&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAnatoly+Maltsev" class="Z3988"></span></span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="https://www.worldcat.org/oclc/299619399">Algorithms and recursive functions</a> in libraries (<a href="/wiki/WorldCat" title="WorldCat">WorldCat</a> catalog)</span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Anatoly_Maltsev&action=edit&section=5" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="https://mathgenealogy.org/id.php?id=17520">Anatolij Ivanovich Mal'tsev</a> at the <a href="/wiki/Mathematics_Genealogy_Project" title="Mathematics Genealogy Project">Mathematics Genealogy Project</a></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFO'ConnorRobertson" class="citation cs2">O'Connor, John J.; <a href="/wiki/Edmund_F._Robertson" title="Edmund F. Robertson">Robertson, Edmund F.</a>, <a rel="nofollow" class="external text" href="https://mathshistory.st-andrews.ac.uk/Biographies/Malcev.html">"Anatoly Ivanovich Malcev"</a>, <i><a href="/wiki/MacTutor_History_of_Mathematics_Archive" title="MacTutor History of Mathematics Archive">MacTutor History of Mathematics Archive</a></i>, <a href="/wiki/University_of_St_Andrews" title="University of St Andrews">University of St Andrews</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Anatoly+Ivanovich+Malcev&rft.btitle=MacTutor+History+of+Mathematics+Archive&rft.pub=University+of+St+Andrews&rft.aulast=O%27Connor&rft.aufirst=John+J.&rft.au=Robertson%2C+Edmund+F.&rft_id=https%3A%2F%2Fmathshistory.st-andrews.ac.uk%2FBiographies%2FMalcev.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAnatoly+Maltsev" class="Z3988"></span></li></ul> <div class="navbox-styles"><style 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href="https://viaf.org/viaf/2557707">VIAF</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="http://id.worldcat.org/fast/123300/">FAST</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://id.oclc.org/worldcat/entity/E39PBJrRhBjhYyxWrRrbb6Xw4q">WorldCat</a></span></li></ul></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">National</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://d-nb.info/gnd/120900491">Germany</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://id.loc.gov/authorities/n83826105">United States</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://catalogue.bnf.fr/ark:/12148/cb124039788">France</a></span></li><li><span class="uid"><a rel="nofollow" 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