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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-azb mw-list-item"><a href="https://azb.wikipedia.org/wiki/%D8%A7%DB%8C%D8%B1%D9%88%DB%8C%D9%86%D9%82_%DA%A9%D8%A7%D9%BE%D9%84%D8%A7%D9%86%D8%B3%DA%A9%DB%8C" title="ایروینق کاپلانسکی – South Azerbaijani" lang="azb" hreflang="azb" data-title="ایروینق کاپلانسکی" data-language-autonym="تۆرکجه" data-language-local-name="South Azerbaijani" class="interlanguage-link-target"><span>تۆرکجه</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Irving_Kaplansky" title="Irving Kaplansky – Catalan" lang="ca" hreflang="ca" data-title="Irving Kaplansky" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Irving_Kaplansky" title="Irving Kaplansky – Czech" lang="cs" hreflang="cs" data-title="Irving Kaplansky" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Irving_Kaplansky" title="Irving Kaplansky – German" lang="de" hreflang="de" data-title="Irving Kaplansky" 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/Irving_Kaplansky" title="Irving Kaplansky – Spanish" lang="es" hreflang="es" data-title="Irving Kaplansky" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%A7%DB%8C%D8%B1%D9%88%DB%8C%D9%86%DA%AF_%DA%A9%D8%A7%D9%BE%D9%84%D8%A7%D9%86%D8%B3%DA%A9%DB%8C" title="ایروینگ کاپلانسکی – Persian" lang="fa" hreflang="fa" data-title="ایروینگ کاپلانسکی" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Irving_Kaplansky" title="Irving Kaplansky – French" lang="fr" hreflang="fr" data-title="Irving Kaplansky" 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%96%B4%EB%B9%99_%EC%BB%A4%ED%94%8C%EB%9E%9C%EC%8A%A4%ED%82%A4" title="어빙 커플랜스키 – Korean" lang="ko" hreflang="ko" data-title="어빙 커플랜스키" 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%BB%D6%80%D5%BE%D5%AB%D5%B6%D5%A3_%D4%BF%D5%A1%D5%BA%D5%AC%D5%A1%D5%B6%D5%BD%D5%AF%D5%AB" title="Իրվինգ Կապլանսկի – Armenian" lang="hy" hreflang="hy" data-title="Իրվինգ Կապլանսկի" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Irving_Kaplansky" title="Irving Kaplansky – Italian" lang="it" hreflang="it" data-title="Irving Kaplansky" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/Irving_Kaplansky" title="Irving Kaplansky – Haitian Creole" lang="ht" hreflang="ht" data-title="Irving Kaplansky" 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-arz mw-list-item"><a href="https://arz.wikipedia.org/wiki/%D8%A7%D9%8A%D8%B1%D9%81%D9%8A%D9%86%D8%AC_%D9%83%D8%A7%D8%A8%D9%84%D8%A7%D9%86%D8%B3%D9%83%D9%89" title="ايرفينج كابلانسكى – Egyptian Arabic" lang="arz" hreflang="arz" data-title="ايرفينج كابلانسكى" data-language-autonym="مصرى" data-language-local-name="Egyptian Arabic" class="interlanguage-link-target"><span>مصرى</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Irving_Kaplansky" title="Irving Kaplansky – Dutch" lang="nl" hreflang="nl" data-title="Irving Kaplansky" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Irving_Kaplansky" title="Irving Kaplansky – Portuguese" lang="pt" hreflang="pt" data-title="Irving Kaplansky" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9A%D0%B0%D0%BF%D0%BB%D0%B0%D0%BD%D1%81%D0%BA%D0%B8%D0%B9,_%D0%98%D1%80%D0%B2%D0%B8%D0%BD%D0%B3" title="Капланский, Ирвинг – Russian" lang="ru" 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.mw-parser-output .infobox-table th,body.skin--responsive .mw-parser-output .infobox-table td{padding-left:inherit;padding-right:inherit}}</style><table class="infobox biography vcard"><tbody><tr><th colspan="2" class="infobox-above" style="font-size:125%;"><div class="fn">Irving Kaplansky</div></th></tr><tr><td colspan="2" class="infobox-image"><span typeof="mw:File"><a href="/wiki/File:Irving_Kaplansky2.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fe/Irving_Kaplansky2.jpg/200px-Irving_Kaplansky2.jpg" decoding="async" width="200" height="139" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/fe/Irving_Kaplansky2.jpg/300px-Irving_Kaplansky2.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/f/fe/Irving_Kaplansky2.jpg 2x" data-file-width="400" data-file-height="277" /></a></span></td></tr><tr><th scope="row" class="infobox-label">Born</th><td class="infobox-data">March 22, 1917<br /><div style="display:inline" class="birthplace"><a href="/wiki/Toronto" title="Toronto">Toronto</a></div></td></tr><tr><th scope="row" class="infobox-label">Died</th><td class="infobox-data">June 25, 2006 (age 89)<br /><div style="display:inline" class="deathplace"><a href="/wiki/Los_Angeles" title="Los Angeles">Los Angeles</a></div></td></tr><tr><th scope="row" class="infobox-label">Nationality</th><td class="infobox-data category">Canadian, American</td></tr><tr><th scope="row" class="infobox-label">Alma mater</th><td class="infobox-data"><a href="/wiki/University_of_Toronto" title="University of Toronto">University of Toronto</a><br /><a href="/wiki/Harvard_University" title="Harvard University">Harvard University</a></td></tr><tr><th scope="row" class="infobox-label">Known for</th><td class="infobox-data"><a href="/wiki/Erd%C5%91s%E2%80%93Kaplansky_theorem" title="Erdős–Kaplansky theorem">Erdős–Kaplansky theorem</a><br /><a href="/wiki/Kaplansky_density_theorem" title="Kaplansky density theorem">Kaplansky density theorem</a><br /><a href="/wiki/Kaplansky%27s_game" title="Kaplansky's game">Kaplansky's game</a><br /><a href="/wiki/Kaplansky%27s_conjecture" class="mw-redirect" title="Kaplansky's conjecture">Kaplansky's conjecture</a><br /><a href="/wiki/Kaplansky%27s_theorem_on_quadratic_forms" title="Kaplansky's theorem on quadratic forms">Kaplansky's theorem on quadratic forms</a><br /><a href="/wiki/Group_theory" title="Group theory">Group theory</a><br /><a href="/wiki/Hilbert_space" title="Hilbert space">Hilbert space</a><br /><a href="/wiki/Ring_theory" title="Ring theory">Ring theory</a><br /><a href="/wiki/Operator_algebras" class="mw-redirect" title="Operator algebras">Operator algebras</a><br /><a href="/wiki/Homological_algebra" title="Homological algebra">Homological algebra</a><br /><a href="/wiki/Topological_algebra" title="Topological algebra">Topological algebra</a><br /><a href="/wiki/Game_theory" title="Game theory">Game theory</a><br /><a href="/wiki/Field_theory_(mathematics)" class="mw-redirect" title="Field theory (mathematics)">Field theory</a></td></tr><tr><th scope="row" class="infobox-label">Awards</th><td class="infobox-data"><a href="/wiki/William_Lowell_Putnam_Mathematical_Competition" title="William Lowell Putnam Mathematical Competition">William Lowell Putnam Mathematical Competition</a> (1938) <br /> <a href="/wiki/Guggenheim_Fellowship" title="Guggenheim Fellowship">Guggenheim Fellowship</a> (1948) <br /> <a href="/wiki/Jeffery%E2%80%93Williams_Prize" title="Jeffery–Williams Prize">Jeffery–Williams Prize</a> (1968) <br />Honorary member of the <a href="/wiki/London_Mathematical_Society" title="London Mathematical Society">London Mathematical Society</a> (1987)<br /><a href="/wiki/Leroy_P._Steele_Prize" title="Leroy P. Steele Prize">Leroy P. Steele Prize</a> (1989)</td></tr><tr><td colspan="2" class="infobox-full-data"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1257001546"><b>Scientific career</b></td></tr><tr><th scope="row" class="infobox-label">Fields</th><td class="infobox-data category"><a href="/wiki/Mathematics" title="Mathematics">Mathematics</a></td></tr><tr><th scope="row" class="infobox-label">Institutions</th><td class="infobox-data"><a href="/wiki/American_Mathematical_Society" title="American Mathematical Society">American Mathematical Society</a><br /><a href="/wiki/Mathematical_Sciences_Research_Institute" class="mw-redirect" title="Mathematical Sciences Research Institute">Mathematical Sciences Research Institute</a><br /><a href="/wiki/Institute_for_Advanced_Study" title="Institute for Advanced Study">Institute for Advanced Study</a><br /><a href="/wiki/University_of_Chicago" title="University of Chicago">University of Chicago</a><br /> <a href="/wiki/Columbia_University" title="Columbia University">Columbia University</a><br /><a href="/wiki/University_of_California,_Berkeley" title="University of California, Berkeley">University of California, Berkeley</a></td></tr><tr><th scope="row" class="infobox-label"><a href="/wiki/Doctoral_advisor" title="Doctoral advisor">Doctoral advisor</a></th><td class="infobox-data"><a href="/wiki/Saunders_Mac_Lane" title="Saunders Mac Lane">Saunders Mac Lane</a></td></tr><tr><th scope="row" class="infobox-label">Doctoral students</th><td class="infobox-data"><a href="/wiki/Hyman_Bass" title="Hyman Bass">Hyman Bass</a><br /><a href="/wiki/Susanna_S._Epp" title="Susanna S. Epp">Susanna S. Epp</a><br /><a href="/wiki/G%C3%BCnter_Lumer" title="Günter Lumer">Günter Lumer</a><br /><a href="/wiki/Eben_Matlis" title="Eben Matlis">Eben Matlis</a><br /><a href="/wiki/Jacob_Matijevic" title="Jacob Matijevic">Jacob Matijevic</a><br /><a href="/wiki/Donald_Samuel_Ornstein" title="Donald Samuel Ornstein">Donald Ornstein</a><br /><a href="/wiki/Ed_Posner" title="Ed Posner">Ed Posner</a><br /><a href="/wiki/Alex_F._T._W._Rosenberg" title="Alex F. T. W. Rosenberg">Alex F. T. W. Rosenberg</a><br /><a href="/wiki/Joseph_J._Rotman" title="Joseph J. Rotman">Joseph J. Rotman</a><br /><a href="/wiki/Judith_D._Sally" title="Judith D. Sally">Judith D. Sally</a><br /><a href="/wiki/Harold_Widom" title="Harold Widom">Harold Widom</a><sup id="cite_ref-mg_1-0" class="reference"><a href="#cite_note-mg-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup></td></tr><tr style="display:none"><td colspan="2"> </td></tr></tbody></table> <p><b>Irving Kaplansky</b> (March 22, 1917 – June 25, 2006) was a <a href="/wiki/Mathematician" title="Mathematician">mathematician</a>, <a href="/wiki/College_professor" class="mw-redirect" title="College professor">college professor</a>, <a href="/wiki/Author" title="Author">author</a>, and amateur <a href="/wiki/Musician" title="Musician">musician</a>.<sup id="cite_ref-www-history.mcs.st-andrews.ac.uk_2-0" class="reference"><a href="#cite_note-www-history.mcs.st-andrews.ac.uk-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </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=Irving_Kaplansky&action=edit&section=1" title="Edit section: Biography"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Kaplansky or "Kap" as his friends and colleagues called him was born in <a href="/wiki/Toronto" title="Toronto">Toronto</a>, <a href="/wiki/Ontario" title="Ontario">Ontario</a>, Canada, to <a href="/wiki/Polish_Jews" class="mw-redirect" title="Polish Jews">Polish-Jewish</a> immigrants;<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><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> his father worked as a tailor, and his mother ran a grocery and, eventually, a chain of bakeries.<sup id="cite_ref-mmp_5-0" class="reference"><a href="#cite_note-mmp-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup><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><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> He went to <a href="/wiki/Harbord_Collegiate_Institute" title="Harbord Collegiate Institute">Harbord Collegiate Institute</a> receiving the Prince of Wales Scholarship as a teenager. He attended the <a href="/wiki/University_of_Toronto" title="University of Toronto">University of Toronto</a> as an undergraduate and finished first in his class for three consecutive years.<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> In his senior year, he competed in the first <a href="/wiki/William_Lowell_Putnam_Mathematical_Competition" title="William Lowell Putnam Mathematical Competition">William Lowell Putnam Mathematical Competition</a>, becoming one of the first five recipients of the Putnam Fellowship, which paid for graduate studies at <a href="/wiki/Harvard_University" title="Harvard University">Harvard University</a>.<sup id="cite_ref-mmp_5-1" class="reference"><a href="#cite_note-mmp-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> Administered by the <a href="/wiki/Mathematical_Association_of_America" title="Mathematical Association of America">Mathematical Association of America</a>, the competition is widely considered to be the most difficult mathematics examination in the world and "its difficulty is such that the median score is often zero or one (out of 120) despite being attempted by students specializing in mathematics."<sup id="cite_ref-d.umn.edu_9-0" class="reference"><a href="#cite_note-d.umn.edu-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p><p>After receiving his <a href="/wiki/Ph.D." class="mw-redirect" title="Ph.D.">Ph.D.</a> from <a href="/wiki/Harvard" class="mw-redirect" title="Harvard">Harvard</a> in 1941<sup id="cite_ref-mg_1-1" class="reference"><a href="#cite_note-mg-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> as <a href="/wiki/Saunders_Mac_Lane" title="Saunders Mac Lane">Saunders Mac Lane</a>'s first student, he remained at Harvard as a <a href="/wiki/Benjamin_Peirce" title="Benjamin Peirce">Benjamin Peirce</a> Instructor, and in 1944 moved with Mac Lane to <a href="/wiki/Columbia_University" title="Columbia University">Columbia University</a> for one year to collaborate on work surrounding <a href="/wiki/World_War_II" title="World War II">World War II</a><sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> working on "miscellaneous studies in mathematics applied to warfare analysis with emphasis upon aerial gunnery, studies of fire control equipment, and rocketry and toss bombing"<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> with the <a href="/wiki/Applied_Mathematics_Panel" title="Applied Mathematics Panel">Applied Mathematics Panel</a>.<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-ReferenceA_13-0" class="reference"><a href="#cite_note-ReferenceA-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> He was a member of the <a href="/wiki/Institute_for_Advanced_Study" title="Institute for Advanced Study">Institute for Advanced Study</a> and attended the 1946 <a href="/wiki/Princeton_University" title="Princeton University">Princeton University</a> Bicentennial.<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> </p><p>He was <a href="/wiki/Professor" title="Professor">professor</a> of mathematics at the <a href="/wiki/University_of_Chicago" title="University of Chicago">University of Chicago</a> from 1945 to 1984, and Chair of the department from 1962 to 1967. In 1968, Kaplansky was presented an honorary doctoral degree from <a href="/wiki/Queen%27s_University_at_Kingston" title="Queen's University at Kingston">Queen's University</a> with the university noting "we honour as a Canadian whose clarity of lectures, elegance of writing, and profundity of research have won him widespread acclaim as the greatest mathematician this country has so far produced."<sup id="cite_ref-ams.org_15-0" class="reference"><a href="#cite_note-ams.org-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> From 1967 to 1969, Kaplansky wrote the mathematics section of <i><a href="/wiki/Encyclop%C3%A6dia_Britannica" title="Encyclopædia Britannica">Encyclopædia Britannica</a></i>.<sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> Kaplansky was the Director of the <a href="/wiki/Mathematical_Sciences_Research_Institute" class="mw-redirect" title="Mathematical Sciences Research Institute">Mathematical Sciences Research Institute</a> from 1984 to 1992, and the President of the <a href="/wiki/American_Mathematical_Society" title="American Mathematical Society">American Mathematical Society</a> from 1985 to 1986.<sup id="cite_ref-19" class="reference"><a href="#cite_note-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> </p><p>Kaplansky was also an accomplished amateur musician. He had <a href="/wiki/Perfect_pitch" class="mw-redirect" title="Perfect pitch">perfect pitch</a>, studied piano until the age of 15, earned money in high school as a dance band musician, taught <a href="/wiki/Tom_Lehrer" title="Tom Lehrer">Tom Lehrer</a>,<sup id="cite_ref-20" class="reference"><a href="#cite_note-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> and played in Harvard's jazz band in graduate school. He also had a regular program on Harvard's student radio station. After moving to the <a href="/wiki/University_of_Chicago" title="University of Chicago">University of Chicago</a>, he stopped playing for two decades, but then returned to music as an accompanist for student-run <a href="/wiki/Gilbert_and_Sullivan" title="Gilbert and Sullivan">Gilbert and Sullivan</a> productions and as a <a href="/wiki/Calliope_(music)" title="Calliope (music)">calliope</a> player in football game parades.<sup id="cite_ref-mmp_5-2" class="reference"><a href="#cite_note-mmp-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> He often composed music based on mathematical themes. One of those compositions, <i>A Song About Pi</i>, is a melody based on assigning notes to the first 14 decimal places of <a href="/wiki/Pi" title="Pi">pi</a>, and has occasionally been performed by his daughter, singer-songwriter <a href="/wiki/Lucy_Kaplansky" title="Lucy Kaplansky">Lucy Kaplansky</a>.<sup id="cite_ref-21" class="reference"><a href="#cite_note-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Mathematical_contributions">Mathematical contributions</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Irving_Kaplansky&action=edit&section=2" title="Edit section: Mathematical contributions"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Kaplansky made major contributions to <a href="/wiki/Group_theory" title="Group theory">group theory</a>, <a href="/wiki/Ring_theory" title="Ring theory">ring theory</a>, the theory of <a href="/wiki/Operator_algebras" class="mw-redirect" title="Operator algebras">operator algebras</a> and <a href="/wiki/Field_theory_(mathematics)" class="mw-redirect" title="Field theory (mathematics)">field theory</a> and created the <a href="/wiki/Kaplansky_density_theorem" title="Kaplansky density theorem">Kaplansky density theorem</a>, <a href="/wiki/Kaplansky%27s_game" title="Kaplansky's game">Kaplansky's game</a> and <a href="/wiki/Kaplansky_conjecture" class="mw-redirect" title="Kaplansky conjecture">Kaplansky conjecture</a>. He published more than 150 articles and 11 mathematical books.<sup id="cite_ref-www-history.mcs.st-andrews.ac.uk_2-1" class="reference"><a href="#cite_note-www-history.mcs.st-andrews.ac.uk-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p><p>Kaplansky was the <a href="/wiki/Doctoral_supervisor" class="mw-redirect" title="Doctoral supervisor">doctoral supervisor</a> of 55 students including notable mathematicians <a href="/wiki/Hyman_Bass" title="Hyman Bass">Hyman Bass</a>, <a href="/wiki/Susanna_S._Epp" title="Susanna S. Epp">Susanna S. Epp</a>, <a href="/wiki/G%C3%BCnter_Lumer" title="Günter Lumer">Günter Lumer</a>, <a href="/wiki/Eben_Matlis" title="Eben Matlis">Eben Matlis</a>, <a href="/wiki/Donald_Samuel_Ornstein" title="Donald Samuel Ornstein">Donald Ornstein</a>, <a href="/wiki/Ed_Posner" title="Ed Posner">Ed Posner</a>, <a href="/wiki/Alex_F._T._W._Rosenberg" title="Alex F. T. W. Rosenberg">Alex F. T. W. Rosenberg</a>, <a href="/wiki/Judith_D._Sally" title="Judith D. Sally">Judith D. Sally</a>, and <a href="/wiki/Harold_Widom" title="Harold Widom">Harold Widom</a>. He has over 950 <a href="/wiki/Academic_genealogy" title="Academic genealogy">academic descendants</a>, including many through his academic grandchildren <a href="/wiki/David_J._Foulis" title="David J. Foulis">David J. Foulis</a> (who studied with Kaplansky at the University of Chicago before completing his doctorate under the supervision of Kaplansky's student Fred Wright, Jr.) and <a href="/wiki/Carl_Pearcy" title="Carl Pearcy">Carl Pearcy</a> (the student of H. Arlen Brown, who had been jointly supervised by Kaplansky and <a href="/wiki/Paul_Halmos" title="Paul Halmos">Paul Halmos</a>).<sup id="cite_ref-mg_1-2" class="reference"><a href="#cite_note-mg-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Awards_and_honors">Awards and honors</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Irving_Kaplansky&action=edit&section=3" title="Edit section: Awards and honors"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Kaplansky was a member of the <a href="/wiki/United_States_National_Academy_of_Sciences" class="mw-redirect" title="United States National Academy of Sciences">National Academy of Sciences</a> and the <a href="/wiki/American_Academy_of_Arts_and_Sciences" title="American Academy of Arts and Sciences">American Academy of Arts and Sciences</a>, Director of the <a href="/wiki/Mathematical_Sciences_Research_Institute" class="mw-redirect" title="Mathematical Sciences Research Institute">Mathematical Sciences Research Institute</a>, and President of the <a href="/wiki/American_Mathematical_Society" title="American Mathematical Society">American Mathematical Society</a>. He was the plenary speaker at the British Mathematical Colloquium in 1966. Won the <a href="/wiki/William_Lowell_Putnam_Mathematical_Competition" title="William Lowell Putnam Mathematical Competition">William Lowell Putnam Mathematical Competition</a>, the <a href="/wiki/Guggenheim_Fellowship" title="Guggenheim Fellowship">Guggenheim Fellowship</a>, the <a href="/wiki/Jeffery%E2%80%93Williams_Prize" title="Jeffery–Williams Prize">Jeffery–Williams Prize</a>, and the <a href="/wiki/Leroy_P._Steele_Prize" title="Leroy P. Steele Prize">Leroy P. Steele Prize</a>.<sup id="cite_ref-ReferenceA_13-1" class="reference"><a href="#cite_note-ReferenceA-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-ams.org_15-1" class="reference"><a href="#cite_note-ams.org-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> </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=Irving_Kaplansky&action=edit&section=4" title="Edit section: Selected publications"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Books">Books</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Irving_Kaplansky&action=edit&section=5" title="Edit section: Books"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><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><cite id="CITEREFKaplansky1954" class="citation book cs1">Kaplansky, Irving (1954). <i>Infinite Abelian groups</i>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Infinite+Abelian+groups&rft.date=1954&rft.aulast=Kaplansky&rft.aufirst=Irving&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIrving+Kaplansky" class="Z3988"></span><sup id="cite_ref-22" class="reference"><a href="#cite_note-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> revised edn. 1971 with several later reprintings</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKaplansky1955" class="citation book cs1">—— (1955). <i>An introduction to differential algebra</i>. University of Chicago Press.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=An+introduction+to+differential+algebra&rft.pub=University+of+Chicago+Press&rft.date=1955&rft.aulast=Kaplansky&rft.aufirst=Irving&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIrving+Kaplansky" class="Z3988"></span> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation book cs1"><i>2nd edn</i>. Paris: Hermann. 1957.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=2nd+edn.&rft.place=Paris&rft.pub=Hermann&rft.date=1957&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIrving+Kaplansky" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKaplansky1966" class="citation book cs1">—— (1966). <i>Introdução à teoria de Galois, por I. Kaplansky. Pref. de <a href="/wiki/Elon_Lages_Lima" title="Elon Lages Lima">Elon Lages Lima</a></i>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Introdu%C3%A7%C3%A3o+%C3%A0+teoria+de+Galois%2C+por+I.+Kaplansky.+Pref.+de+Elon+Lages+Lima&rft.date=1966&rft.aulast=Kaplansky&rft.aufirst=Irving&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIrving+Kaplansky" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKaplansky1968" class="citation book cs1">—— (1968). <i>Rings of operators</i>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Rings+of+operators&rft.date=1968&rft.aulast=Kaplansky&rft.aufirst=Irving&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIrving+Kaplansky" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKaplansky1969" class="citation book cs1">—— (1969). <i>Fields and rings</i>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Fields+and+rings&rft.date=1969&rft.aulast=Kaplansky&rft.aufirst=Irving&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIrving+Kaplansky" class="Z3988"></span> 2nd edn. 1972</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKaplansky1969" class="citation book cs1">—— (1969). <i>Linear algebra and geometry; a second course</i>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Linear+algebra+and+geometry%3B+a+second+course&rft.date=1969&rft.aulast=Kaplansky&rft.aufirst=Irving&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIrving+Kaplansky" class="Z3988"></span> <a rel="nofollow" class="external text" href="https://books.google.com/books/about/Linear_Algebra_and_Geometry.html?id=nUcUYHrYJtgC">revised edn. 1974</a></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKaplansky1970" class="citation book cs1">—— (1970). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=K4K4zn2pME8C"><i>Algebraic and analytic aspects of operator algebras</i></a>. American Mathematical Soc. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780821816509" title="Special:BookSources/9780821816509"><bdi>9780821816509</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Algebraic+and+analytic+aspects+of+operator+algebras&rft.pub=American+Mathematical+Soc.&rft.date=1970&rft.isbn=9780821816509&rft.aulast=Kaplansky&rft.aufirst=Irving&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DK4K4zn2pME8C&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIrving+Kaplansky" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKaplansky1971" class="citation book cs1">—— (1971). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=KUJXxxYiGPsC"><i>Lie Algebras and Locally Compact Groups</i></a>. <a href="/wiki/University_of_Chicago_Press" title="University of Chicago Press">University of Chicago Press</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-226-42453-7" title="Special:BookSources/0-226-42453-7"><bdi>0-226-42453-7</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Lie+Algebras+and+Locally+Compact+Groups&rft.pub=University+of+Chicago+Press&rft.date=1971&rft.isbn=0-226-42453-7&rft.aulast=Kaplansky&rft.aufirst=Irving&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DKUJXxxYiGPsC&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIrving+Kaplansky" class="Z3988"></span> several later reprintings</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKaplansky1972" class="citation book cs1">—— (1972). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/settheorymetrics0000kapl"><i>Set theory and metric spaces</i></a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Set+theory+and+metric+spaces&rft.date=1972&rft.aulast=Kaplansky&rft.aufirst=Irving&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fsettheorymetrics0000kapl&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIrving+Kaplansky" class="Z3988"></span> <a rel="nofollow" class="external text" href="https://books.google.com/books/about/Set_Theory_and_Metric_Spaces.html?id=1XFDM75VK5MC">2nd edn. 1977</a></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKaplansky1974" class="citation book cs1">—— (September 1974). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/commutativerings00irvi"><i>Commutative Rings</i></a></span>. Lectures in Mathematics. University of Chicago Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-226-42454-5" title="Special:BookSources/0-226-42454-5"><bdi>0-226-42454-5</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Commutative+Rings&rft.series=Lectures+in+Mathematics&rft.pub=University+of+Chicago+Press&rft.date=1974-09&rft.isbn=0-226-42454-5&rft.aulast=Kaplansky&rft.aufirst=Irving&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fcommutativerings00irvi&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIrving+Kaplansky" class="Z3988"></span> 1st edn. 1966; revised 1974 with several later reprintings</li></ul> <p>with I. N. Herstein: <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKaplansky1974" class="citation book cs1">—— (1974). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/mattersmathemati00hers"><i>Matters mathematical</i></a></span>. New York, Harper & Row. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780060428037" title="Special:BookSources/9780060428037"><bdi>9780060428037</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Matters+mathematical&rft.pub=New+York%2C+Harper+%26+Row&rft.date=1974&rft.isbn=9780060428037&rft.aulast=Kaplansky&rft.aufirst=Irving&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fmattersmathemati00hers&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIrving+Kaplansky" class="Z3988"></span> <a rel="nofollow" class="external text" href="https://books.google.com/books/about/Matters_Mathematical.html?id=cxW2vicWG3AC">2nd edn. 1978</a> </p> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKaplansky1995" class="citation book cs1">Kaplansky, Irving (1995). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=VVY_9yWl33YC"><i>Selected papers and other writings</i></a>. Springer. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780387944067" title="Special:BookSources/9780387944067"><bdi>9780387944067</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Selected+papers+and+other+writings&rft.pub=Springer&rft.date=1995&rft.isbn=9780387944067&rft.aulast=Kaplansky&rft.aufirst=Irving&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DVVY_9yWl33YC&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIrving+Kaplansky" class="Z3988"></span></li></ul> <div class="mw-heading mw-heading3"><h3 id="Articles">Articles</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Irving_Kaplansky&action=edit&section=6" title="Edit section: Articles"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKaplansky1944" class="citation journal cs1">Kaplansky, Irving (1944). <a rel="nofollow" class="external text" href="https://doi.org/10.1090%2Fs0002-9904-1944-08261-x">"Symbolic solution of certain problems in permutations"</a>. <i>Bull. Amer. Math. Soc</i>. <b>50</b> (12): 906–914. <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%2Fs0002-9904-1944-08261-x">10.1090/s0002-9904-1944-08261-x</a></span>. <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=0011393">0011393</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Bull.+Amer.+Math.+Soc.&rft.atitle=Symbolic+solution+of+certain+problems+in+permutations&rft.volume=50&rft.issue=12&rft.pages=906-914&rft.date=1944&rft_id=info%3Adoi%2F10.1090%2Fs0002-9904-1944-08261-x&rft_id=https%3A%2F%2Fmathscinet.ams.org%2Fmathscinet-getitem%3Fmr%3D0011393%23id-name%3DMR&rft.aulast=Kaplansky&rft.aufirst=Irving&rft_id=https%3A%2F%2Fdoi.org%2F10.1090%252Fs0002-9904-1944-08261-x&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIrving+Kaplansky" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKaplansky1945" class="citation journal cs1">Kaplansky, Irving (1945). <a rel="nofollow" class="external text" href="https://doi.org/10.1090%2Fs0002-9904-1945-08382-7">"A note on groups without isomorphic subgroups"</a>. <i>Bull. Amer. Math. Soc</i>. <b>51</b> (8): 529–530. <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%2Fs0002-9904-1945-08382-7">10.1090/s0002-9904-1945-08382-7</a></span>. <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=0012267">0012267</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Bull.+Amer.+Math.+Soc.&rft.atitle=A+note+on+groups+without+isomorphic+subgroups&rft.volume=51&rft.issue=8&rft.pages=529-530&rft.date=1945&rft_id=info%3Adoi%2F10.1090%2Fs0002-9904-1945-08382-7&rft_id=https%3A%2F%2Fmathscinet.ams.org%2Fmathscinet-getitem%3Fmr%3D0012267%23id-name%3DMR&rft.aulast=Kaplansky&rft.aufirst=Irving&rft_id=https%3A%2F%2Fdoi.org%2F10.1090%252Fs0002-9904-1945-08382-7&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIrving+Kaplansky" class="Z3988"></span></li> <li>with <a href="/wiki/Irvin_Cohen" title="Irvin Cohen">I. S. Cohen</a>: <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCohenKaplansky1946" class="citation journal cs1">Cohen, I. S.; Kaplansky, Irving (1946). <a rel="nofollow" class="external text" href="https://doi.org/10.1090%2Fs0002-9947-1946-0019595-7">"Rings with a finite number of primes. I"</a>. <i>Trans. Amer. Math. Soc</i>. <b>60</b>: 468–477. <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%2Fs0002-9947-1946-0019595-7">10.1090/s0002-9947-1946-0019595-7</a></span>. <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=0019595">0019595</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Trans.+Amer.+Math.+Soc.&rft.atitle=Rings+with+a+finite+number+of+primes.+I&rft.volume=60&rft.pages=468-477&rft.date=1946&rft_id=info%3Adoi%2F10.1090%2Fs0002-9947-1946-0019595-7&rft_id=https%3A%2F%2Fmathscinet.ams.org%2Fmathscinet-getitem%3Fmr%3D0019595%23id-name%3DMR&rft.aulast=Cohen&rft.aufirst=I.+S.&rft.au=Kaplansky%2C+Irving&rft_id=https%3A%2F%2Fdoi.org%2F10.1090%252Fs0002-9947-1946-0019595-7&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIrving+Kaplansky" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKaplansky1946" class="citation journal cs1">Kaplansky, Irving (1946). <a rel="nofollow" class="external text" href="https://doi.org/10.1090%2Fs0002-9904-1946-08600-0">"On a problem of Kurosch and Jacobson"</a>. <i>Bull. Amer. Math. Soc</i>. <b>52</b> (6): 496–500. <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%2Fs0002-9904-1946-08600-0">10.1090/s0002-9904-1946-08600-0</a></span>. <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=0016758">0016758</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Bull.+Amer.+Math.+Soc.&rft.atitle=On+a+problem+of+Kurosch+and+Jacobson&rft.volume=52&rft.issue=6&rft.pages=496-500&rft.date=1946&rft_id=info%3Adoi%2F10.1090%2Fs0002-9904-1946-08600-0&rft_id=https%3A%2F%2Fmathscinet.ams.org%2Fmathscinet-getitem%3Fmr%3D0016758%23id-name%3DMR&rft.aulast=Kaplansky&rft.aufirst=Irving&rft_id=https%3A%2F%2Fdoi.org%2F10.1090%252Fs0002-9904-1946-08600-0&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIrving+Kaplansky" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKaplansky1947" class="citation journal cs1">Kaplansky, Irving (1947). <a rel="nofollow" class="external text" href="https://doi.org/10.1090%2Fs0002-9904-1947-08856-x">"Lattices of continuous functions"</a>. <i>Bull. Amer. Math. Soc</i>. <b>53</b> (6): 617–623. <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%2Fs0002-9904-1947-08856-x">10.1090/s0002-9904-1947-08856-x</a></span>. <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=0020715">0020715</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Bull.+Amer.+Math.+Soc.&rft.atitle=Lattices+of+continuous+functions&rft.volume=53&rft.issue=6&rft.pages=617-623&rft.date=1947&rft_id=info%3Adoi%2F10.1090%2Fs0002-9904-1947-08856-x&rft_id=https%3A%2F%2Fmathscinet.ams.org%2Fmathscinet-getitem%3Fmr%3D0020715%23id-name%3DMR&rft.aulast=Kaplansky&rft.aufirst=Irving&rft_id=https%3A%2F%2Fdoi.org%2F10.1090%252Fs0002-9904-1947-08856-x&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIrving+Kaplansky" class="Z3988"></span></li> <li>with <a href="/wiki/Richard_Friederich_Arens" title="Richard Friederich Arens">Richard F. Arens</a>: <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFArensKaplansky1948" class="citation journal cs1">Arens, Richard F.; Kaplansky, Irving (1948). <a rel="nofollow" class="external text" href="https://doi.org/10.1090%2Fs0002-9947-1948-0025453-6">"Topological representations of algebras"</a>. <i>Trans. Amer. Math. Soc</i>. <b>63</b> (3): 457–481. <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%2Fs0002-9947-1948-0025453-6">10.1090/s0002-9947-1948-0025453-6</a></span>. <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=0025453">0025453</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Trans.+Amer.+Math.+Soc.&rft.atitle=Topological+representations+of+algebras&rft.volume=63&rft.issue=3&rft.pages=457-481&rft.date=1948&rft_id=info%3Adoi%2F10.1090%2Fs0002-9947-1948-0025453-6&rft_id=https%3A%2F%2Fmathscinet.ams.org%2Fmathscinet-getitem%3Fmr%3D0025453%23id-name%3DMR&rft.aulast=Arens&rft.aufirst=Richard+F.&rft.au=Kaplansky%2C+Irving&rft_id=https%3A%2F%2Fdoi.org%2F10.1090%252Fs0002-9947-1948-0025453-6&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIrving+Kaplansky" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKaplansky1948" class="citation journal cs1">Kaplansky, Irving (1948). <a rel="nofollow" class="external text" href="https://doi.org/10.1090%2Fs0002-9904-1948-09049-8">"Rings with a polynomial identity"</a>. <i>Bull. Amer. Math. Soc</i>. <b>54</b> (6): 575–580. <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%2Fs0002-9904-1948-09049-8">10.1090/s0002-9904-1948-09049-8</a></span>. <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=0025451">0025451</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Bull.+Amer.+Math.+Soc.&rft.atitle=Rings+with+a+polynomial+identity&rft.volume=54&rft.issue=6&rft.pages=575-580&rft.date=1948&rft_id=info%3Adoi%2F10.1090%2Fs0002-9904-1948-09049-8&rft_id=https%3A%2F%2Fmathscinet.ams.org%2Fmathscinet-getitem%3Fmr%3D0025451%23id-name%3DMR&rft.aulast=Kaplansky&rft.aufirst=Irving&rft_id=https%3A%2F%2Fdoi.org%2F10.1090%252Fs0002-9904-1948-09049-8&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIrving+Kaplansky" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation journal cs1"><a rel="nofollow" class="external text" href="https://doi.org/10.1090%2FS0002-9904-1948-09096-6">"Topological rings"</a>. <i>Bull. Amer. Math. Soc</i>. <b>54</b>: 909–916. 1948. <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%2FS0002-9904-1948-09096-6">10.1090/S0002-9904-1948-09096-6</a></span>. <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=0027269">0027269</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Bull.+Amer.+Math.+Soc.&rft.atitle=Topological+rings&rft.volume=54&rft.pages=909-916&rft.date=1948&rft_id=info%3Adoi%2F10.1090%2FS0002-9904-1948-09096-6&rft_id=https%3A%2F%2Fmathscinet.ams.org%2Fmathscinet-getitem%3Fmr%3D0027269%23id-name%3DMR&rft_id=https%3A%2F%2Fdoi.org%2F10.1090%252FS0002-9904-1948-09096-6&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIrving+Kaplansky" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKaplansky1949" class="citation journal cs1">Kaplansky, Irving (1949). <a rel="nofollow" class="external text" href="https://doi.org/10.1090%2Fs0002-9947-1949-0031470-3">"Elementary divisors and modules"</a>. <i>Trans. Amer. Math. Soc</i>. <b>66</b> (2): 464–491. <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%2Fs0002-9947-1949-0031470-3">10.1090/s0002-9947-1949-0031470-3</a></span>. <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=0031470">0031470</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Trans.+Amer.+Math.+Soc.&rft.atitle=Elementary+divisors+and+modules&rft.volume=66&rft.issue=2&rft.pages=464-491&rft.date=1949&rft_id=info%3Adoi%2F10.1090%2Fs0002-9947-1949-0031470-3&rft_id=https%3A%2F%2Fmathscinet.ams.org%2Fmathscinet-getitem%3Fmr%3D0031470%23id-name%3DMR&rft.aulast=Kaplansky&rft.aufirst=Irving&rft_id=https%3A%2F%2Fdoi.org%2F10.1090%252Fs0002-9947-1949-0031470-3&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIrving+Kaplansky" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKaplansky1949" class="citation journal cs1">Kaplansky, I. (1949). <a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1062983">"Primary ideals in group algebras"</a>. <i>Proc Natl Acad Sci U S A</i>. <b>35</b> (3): 133–136. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1949PNAS...35..133K">1949PNAS...35..133K</a>. <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/10.1073%2Fpnas.35.3.133">10.1073/pnas.35.3.133</a></span>. <a href="/wiki/PMC_(identifier)" class="mw-redirect" title="PMC (identifier)">PMC</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1062983">1062983</a></span>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/16588871">16588871</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Proc+Natl+Acad+Sci+U+S+A&rft.atitle=Primary+ideals+in+group+algebras&rft.volume=35&rft.issue=3&rft.pages=133-136&rft.date=1949&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC1062983%23id-name%3DPMC&rft_id=info%3Apmid%2F16588871&rft_id=info%3Adoi%2F10.1073%2Fpnas.35.3.133&rft_id=info%3Abibcode%2F1949PNAS...35..133K&rft.aulast=Kaplansky&rft.aufirst=I.&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC1062983&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIrving+Kaplansky" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKaplansky1950" class="citation journal cs1">Kaplansky, Irving (1950). <a rel="nofollow" class="external text" href="https://doi.org/10.1090%2Fs0002-9947-1950-0032612-4">"Topological representations of algebras. II"</a>. <i>Trans. Amer. Math. Soc</i>. <b>68</b>: 62–75. <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%2Fs0002-9947-1950-0032612-4">10.1090/s0002-9947-1950-0032612-4</a></span>. <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=0032612">0032612</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Trans.+Amer.+Math.+Soc.&rft.atitle=Topological+representations+of+algebras.+II&rft.volume=68&rft.pages=62-75&rft.date=1950&rft_id=info%3Adoi%2F10.1090%2Fs0002-9947-1950-0032612-4&rft_id=https%3A%2F%2Fmathscinet.ams.org%2Fmathscinet-getitem%3Fmr%3D0032612%23id-name%3DMR&rft.aulast=Kaplansky&rft.aufirst=Irving&rft_id=https%3A%2F%2Fdoi.org%2F10.1090%252Fs0002-9947-1950-0032612-4&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIrving+Kaplansky" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKaplansky1950" class="citation journal cs1">Kaplansky, Irving (1950). <a rel="nofollow" class="external text" href="https://doi.org/10.1090%2Fs0002-9939-1950-0035760-3">"The Weierstrass theorem in fields with valuations"</a>. <i>Proc. Amer. Math. Soc</i>. <b>1</b> (3): 356–357. <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%2Fs0002-9939-1950-0035760-3">10.1090/s0002-9939-1950-0035760-3</a></span>. <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=0035760">0035760</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Proc.+Amer.+Math.+Soc.&rft.atitle=The+Weierstrass+theorem+in+fields+with+valuations&rft.volume=1&rft.issue=3&rft.pages=356-357&rft.date=1950&rft_id=info%3Adoi%2F10.1090%2Fs0002-9939-1950-0035760-3&rft_id=https%3A%2F%2Fmathscinet.ams.org%2Fmathscinet-getitem%3Fmr%3D0035760%23id-name%3DMR&rft.aulast=Kaplansky&rft.aufirst=Irving&rft_id=https%3A%2F%2Fdoi.org%2F10.1090%252Fs0002-9939-1950-0035760-3&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIrving+Kaplansky" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKaplansky1951" class="citation journal cs1">Kaplansky, Irving (1951). <a rel="nofollow" class="external text" href="https://doi.org/10.1090%2Fs0002-9947-1951-0042066-0">"The structure of certain operator algebras"</a>. <i>Trans. Amer. Math. Soc</i>. <b>70</b> (2): 219–255. <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%2Fs0002-9947-1951-0042066-0">10.1090/s0002-9947-1951-0042066-0</a></span>. <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=0042066">0042066</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Trans.+Amer.+Math.+Soc.&rft.atitle=The+structure+of+certain+operator+algebras&rft.volume=70&rft.issue=2&rft.pages=219-255&rft.date=1951&rft_id=info%3Adoi%2F10.1090%2Fs0002-9947-1951-0042066-0&rft_id=https%3A%2F%2Fmathscinet.ams.org%2Fmathscinet-getitem%3Fmr%3D0042066%23id-name%3DMR&rft.aulast=Kaplansky&rft.aufirst=Irving&rft_id=https%3A%2F%2Fdoi.org%2F10.1090%252Fs0002-9947-1951-0042066-0&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIrving+Kaplansky" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKaplansky1952" class="citation journal cs1">Kaplansky, Irving (1952). <a rel="nofollow" class="external text" href="https://doi.org/10.1090%2Fs0002-9947-1952-0046349-0">"Modules over Dedekind rings and valuations rings"</a>. <i>Trans. Amer. Math. Soc</i>. <b>72</b> (2): 327–340. <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%2Fs0002-9947-1952-0046349-0">10.1090/s0002-9947-1952-0046349-0</a></span>. <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=0046349">0046349</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Trans.+Amer.+Math.+Soc.&rft.atitle=Modules+over+Dedekind+rings+and+valuations+rings&rft.volume=72&rft.issue=2&rft.pages=327-340&rft.date=1952&rft_id=info%3Adoi%2F10.1090%2Fs0002-9947-1952-0046349-0&rft_id=https%3A%2F%2Fmathscinet.ams.org%2Fmathscinet-getitem%3Fmr%3D0046349%23id-name%3DMR&rft.aulast=Kaplansky&rft.aufirst=Irving&rft_id=https%3A%2F%2Fdoi.org%2F10.1090%252Fs0002-9947-1952-0046349-0&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIrving+Kaplansky" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKaplansky1952" class="citation journal cs1">Kaplansky, Irving (1952). <a rel="nofollow" class="external text" href="https://doi.org/10.1090%2Fs0002-9939-1952-0046564-1">"Orthogonal similarity in infinite dimensional spaces"</a>. <i>Proc. Amer. Math. Soc</i>. <b>3</b>: 16–25. <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%2Fs0002-9939-1952-0046564-1">10.1090/s0002-9939-1952-0046564-1</a></span>. <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=0046564">0046564</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Proc.+Amer.+Math.+Soc.&rft.atitle=Orthogonal+similarity+in+infinite+dimensional+spaces&rft.volume=3&rft.pages=16-25&rft.date=1952&rft_id=info%3Adoi%2F10.1090%2Fs0002-9939-1952-0046564-1&rft_id=https%3A%2F%2Fmathscinet.ams.org%2Fmathscinet-getitem%3Fmr%3D0046564%23id-name%3DMR&rft.aulast=Kaplansky&rft.aufirst=Irving&rft_id=https%3A%2F%2Fdoi.org%2F10.1090%252Fs0002-9939-1952-0046564-1&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIrving+Kaplansky" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKaplansky1952" class="citation journal cs1">Kaplansky, Irving (1952). <a rel="nofollow" class="external text" href="https://doi.org/10.1090%2Fs0002-9939-1952-0048711-4">"Symmetry of Banach algebras"</a>. <i>Proc. Amer. Math. Soc</i>. <b>3</b> (3): 396–399. <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%2Fs0002-9939-1952-0048711-4">10.1090/s0002-9939-1952-0048711-4</a></span>. <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=0048711">0048711</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Proc.+Amer.+Math.+Soc.&rft.atitle=Symmetry+of+Banach+algebras&rft.volume=3&rft.issue=3&rft.pages=396-399&rft.date=1952&rft_id=info%3Adoi%2F10.1090%2Fs0002-9939-1952-0048711-4&rft_id=https%3A%2F%2Fmathscinet.ams.org%2Fmathscinet-getitem%3Fmr%3D0048711%23id-name%3DMR&rft.aulast=Kaplansky&rft.aufirst=Irving&rft_id=https%3A%2F%2Fdoi.org%2F10.1090%252Fs0002-9939-1952-0048711-4&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIrving+Kaplansky" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKaplansky1952" class="citation journal cs1">Kaplansky, I. (1952). <a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1063607">"Some results on abelian groups"</a>. <i>Proc Natl Acad Sci U S A</i>. <b>38</b> (6): 538–540. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1952PNAS...38..538K">1952PNAS...38..538K</a>. <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/10.1073%2Fpnas.38.6.538">10.1073/pnas.38.6.538</a></span>. <a href="/wiki/PMC_(identifier)" class="mw-redirect" title="PMC (identifier)">PMC</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1063607">1063607</a></span>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/16589142">16589142</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Proc+Natl+Acad+Sci+U+S+A&rft.atitle=Some+results+on+abelian+groups&rft.volume=38&rft.issue=6&rft.pages=538-540&rft.date=1952&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC1063607%23id-name%3DPMC&rft_id=info%3Apmid%2F16589142&rft_id=info%3Adoi%2F10.1073%2Fpnas.38.6.538&rft_id=info%3Abibcode%2F1952PNAS...38..538K&rft.aulast=Kaplansky&rft.aufirst=I.&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC1063607&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIrving+Kaplansky" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKaplansky1953" class="citation journal cs1">Kaplansky, Irving (1953). <a rel="nofollow" class="external text" href="https://doi.org/10.1090%2Fs0002-9939-1953-0059895-7">"Infinite dimensional quadratic forms admitting composition"</a>. <i>Proc. Amer. Math. Soc</i>. <b>4</b> (6): 956–960. <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%2Fs0002-9939-1953-0059895-7">10.1090/s0002-9939-1953-0059895-7</a></span>. <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=0059895">0059895</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Proc.+Amer.+Math.+Soc.&rft.atitle=Infinite+dimensional+quadratic+forms+admitting+composition&rft.volume=4&rft.issue=6&rft.pages=956-960&rft.date=1953&rft_id=info%3Adoi%2F10.1090%2Fs0002-9939-1953-0059895-7&rft_id=https%3A%2F%2Fmathscinet.ams.org%2Fmathscinet-getitem%3Fmr%3D0059895%23id-name%3DMR&rft.aulast=Kaplansky&rft.aufirst=Irving&rft_id=https%3A%2F%2Fdoi.org%2F10.1090%252Fs0002-9939-1953-0059895-7&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIrving+Kaplansky" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKaplansky1953" class="citation journal cs1">Kaplansky, Irving (1953). <a rel="nofollow" class="external text" href="https://doi.org/10.1090%2Fs0002-9939-1953-0053092-7">"Dual modules over a valuation ring. I"</a>. <i>Proc. Amer. Math. Soc</i>. <b>4</b> (2): 213–219. <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%2Fs0002-9939-1953-0053092-7">10.1090/s0002-9939-1953-0053092-7</a></span>. <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=0053092">0053092</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Proc.+Amer.+Math.+Soc.&rft.atitle=Dual+modules+over+a+valuation+ring.+I&rft.volume=4&rft.issue=2&rft.pages=213-219&rft.date=1953&rft_id=info%3Adoi%2F10.1090%2Fs0002-9939-1953-0053092-7&rft_id=https%3A%2F%2Fmathscinet.ams.org%2Fmathscinet-getitem%3Fmr%3D0053092%23id-name%3DMR&rft.aulast=Kaplansky&rft.aufirst=Irving&rft_id=https%3A%2F%2Fdoi.org%2F10.1090%252Fs0002-9939-1953-0053092-7&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIrving+Kaplansky" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKaplansky1958" class="citation journal cs1">Kaplansky, Irving (1958). <a rel="nofollow" class="external text" href="https://doi.org/10.1090%2Fs0002-9947-1958-0099359-7">"Lie algebras of characteristic <i>p</i>"</a>. <i>Trans. Amer. Math. Soc</i>. <b>89</b>: 149–183. <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%2Fs0002-9947-1958-0099359-7">10.1090/s0002-9947-1958-0099359-7</a></span>. <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=0099359">0099359</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Trans.+Amer.+Math.+Soc.&rft.atitle=Lie+algebras+of+characteristic+p&rft.volume=89&rft.pages=149-183&rft.date=1958&rft_id=info%3Adoi%2F10.1090%2Fs0002-9947-1958-0099359-7&rft_id=https%3A%2F%2Fmathscinet.ams.org%2Fmathscinet-getitem%3Fmr%3D0099359%23id-name%3DMR&rft.aulast=Kaplansky&rft.aufirst=Irving&rft_id=https%3A%2F%2Fdoi.org%2F10.1090%252Fs0002-9947-1958-0099359-7&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIrving+Kaplansky" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKaplansky1962" class="citation journal cs1">Kaplansky, Irving (1962). <a rel="nofollow" class="external text" href="https://doi.org/10.1090%2Fs0002-9939-1962-0137738-6">"Decomposability of modules"</a>. <i>Proc. Amer. Math. Soc</i>. <b>13</b> (4): 532–535. <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%2Fs0002-9939-1962-0137738-6">10.1090/s0002-9939-1962-0137738-6</a></span>. <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=0137738">0137738</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Proc.+Amer.+Math.+Soc.&rft.atitle=Decomposability+of+modules&rft.volume=13&rft.issue=4&rft.pages=532-535&rft.date=1962&rft_id=info%3Adoi%2F10.1090%2Fs0002-9939-1962-0137738-6&rft_id=https%3A%2F%2Fmathscinet.ams.org%2Fmathscinet-getitem%3Fmr%3D0137738%23id-name%3DMR&rft.aulast=Kaplansky&rft.aufirst=Irving&rft_id=https%3A%2F%2Fdoi.org%2F10.1090%252Fs0002-9939-1962-0137738-6&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIrving+Kaplansky" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKaplansky1980" class="citation journal cs1">Kaplansky, Irving (1980). <a rel="nofollow" class="external text" href="http://projecteuclid.org/euclid.pjm/1102780617">"Superalgebras"</a>. <i>Pacific J. Math</i>. <b>86</b> (1): 93–98. <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/10.2140%2Fpjm.1980.86.93">10.2140/pjm.1980.86.93</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Pacific+J.+Math.&rft.atitle=Superalgebras&rft.volume=86&rft.issue=1&rft.pages=93-98&rft.date=1980&rft_id=info%3Adoi%2F10.2140%2Fpjm.1980.86.93&rft.aulast=Kaplansky&rft.aufirst=Irving&rft_id=http%3A%2F%2Fprojecteuclid.org%2Feuclid.pjm%2F1102780617&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIrving+Kaplansky" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKaplansky1994" class="citation journal cs1">Kaplansky, Irving (1994). <a rel="nofollow" class="external text" href="https://doi.org/10.1090%2Fs0002-9939-1994-1257114-3">"A quasi-commutative ring that is not neo-commutative"</a>. <i>Proc. Amer. Math. Soc</i>. <b>122</b>: 321. <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%2Fs0002-9939-1994-1257114-3">10.1090/s0002-9939-1994-1257114-3</a></span>. <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=1257114">1257114</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Proc.+Amer.+Math.+Soc.&rft.atitle=A+quasi-commutative+ring+that+is+not+neo-commutative&rft.volume=122&rft.pages=321&rft.date=1994&rft_id=info%3Adoi%2F10.1090%2Fs0002-9939-1994-1257114-3&rft_id=https%3A%2F%2Fmathscinet.ams.org%2Fmathscinet-getitem%3Fmr%3D1257114%23id-name%3DMR&rft.aulast=Kaplansky&rft.aufirst=Irving&rft_id=https%3A%2F%2Fdoi.org%2F10.1090%252Fs0002-9939-1994-1257114-3&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIrving+Kaplansky" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation journal cs1"><a rel="nofollow" class="external text" href="https://doi.org/10.1090%2Fs0002-9939-03-07022-9">"The forms <i>x</i>+32<i>y</i><sup>2</sup> and <i>x</i>+64<i>y</i><sup>2 </sup>"</a>. <i>Proc. Amer. Math. Soc</i>. <b>131</b>: 2299–2300. 2003. <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%2Fs0002-9939-03-07022-9">10.1090/s0002-9939-03-07022-9</a></span>. <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=1963780">1963780</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Proc.+Amer.+Math.+Soc.&rft.atitle=The+forms+x%2B32y%3Csup%3E2%3C%2Fsup%3E+and+x%2B64y%3Csup%3E2+%3C%2Fsup%3E&rft.volume=131&rft.pages=2299-2300&rft.date=2003&rft_id=info%3Adoi%2F10.1090%2Fs0002-9939-03-07022-9&rft_id=https%3A%2F%2Fmathscinet.ams.org%2Fmathscinet-getitem%3Fmr%3D1963780%23id-name%3DMR&rft_id=https%3A%2F%2Fdoi.org%2F10.1090%252Fs0002-9939-03-07022-9&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIrving+Kaplansky" class="Z3988"></span></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=Irving_Kaplansky&action=edit&section=7" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Kaplansky%27s_theorem_on_projective_modules" title="Kaplansky's theorem on projective modules">Kaplansky's theorem on projective modules</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Notes">Notes</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Irving_Kaplansky&action=edit&section=8" title="Edit section: Notes"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-mg-1"><span class="mw-cite-backlink">^ <a href="#cite_ref-mg_1-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-mg_1-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-mg_1-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><a rel="nofollow" class="external text" href="https://mathgenealogy.org/id.php?id=833">Irving Kaplansky</a> at the <a href="/wiki/Mathematics_Genealogy_Project" title="Mathematics Genealogy Project">Mathematics Genealogy Project</a></span> </li> <li id="cite_note-www-history.mcs.st-andrews.ac.uk-2"><span class="mw-cite-backlink">^ <a href="#cite_ref-www-history.mcs.st-andrews.ac.uk_2-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-www-history.mcs.st-andrews.ac.uk_2-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text">O'Connor, John J.; Robertson, Edmund F., "Irving Kaplansky", MacTutor History of Mathematics archive, University of St Andrews. <a rel="nofollow" class="external free" href="http://www-history.mcs.st-andrews.ac.uk/Biographies/Kaplansky.html">http://www-history.mcs.st-andrews.ac.uk/Biographies/Kaplansky.html</a>.</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 class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20100618143026/http://zakuski.utsa.edu/~kap/in_memoriam_by_Nancy_Albert.pdf">"Irving Kaplansky Memoir by Nancy E. Albert"</a> <span class="cs1-format">(PDF)</span>. Archived from <a rel="nofollow" class="external text" href="http://zakuski.utsa.edu/~kap/in_memoriam_by_Nancy_Albert.pdf">the original</a> <span class="cs1-format">(PDF)</span> on 2010-06-18<span class="reference-accessdate">. Retrieved <span class="nowrap">2012-11-27</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Irving+Kaplansky+Memoir+by+Nancy+E.+Albert&rft_id=http%3A%2F%2Fzakuski.utsa.edu%2F~kap%2Fin_memoriam_by_Nancy_Albert.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIrving+Kaplansky" 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="CITEREFDecember_4Rothman" class="citation web cs1">December 4; Rothman, 2012 Ellen K. <a rel="nofollow" class="external text" href="https://jwa.org/blog/making-family-stories-into-art">"Making Family Stories into Art"</a>. <i>Jewish Women's Archive</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2022-10-07</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Jewish+Women%27s+Archive&rft.atitle=Making+Family+Stories+into+Art&rft.au=December+4&rft.au=Rothman%2C+2012+Ellen+K.&rft_id=https%3A%2F%2Fjwa.org%2Fblog%2Fmaking-family-stories-into-art&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIrving+Kaplansky" class="Z3988"></span><span class="cs1-maint citation-comment"><code class="cs1-code">{{<a href="/wiki/Template:Cite_web" title="Template:Cite web">cite web</a>}}</code>: CS1 maint: numeric names: authors list (<a href="/wiki/Category:CS1_maint:_numeric_names:_authors_list" title="Category:CS1 maint: numeric names: authors list">link</a>)</span></span> </li> <li id="cite_note-mmp-5"><span class="mw-cite-backlink">^ <a href="#cite_ref-mmp_5-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-mmp_5-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-mmp_5-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAlbersAlexandersonReid1990" class="citation cs2">Albers, Donald J.; <a href="/wiki/Gerald_L._Alexanderson" title="Gerald L. Alexanderson">Alexanderson, Gerald L.</a>; <a href="/wiki/Constance_Reid" title="Constance Reid">Reid, Constance</a>, eds. (1990), "Irving Kaplansky", <a rel="nofollow" class="external text" href="https://books.google.com/books?id=Nu_uAAAAMAAJ"><i>More Mathematical People</i></a>, Harcourt Brace Jovanovich, pp. 118–136, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780120482511" title="Special:BookSources/9780120482511"><bdi>9780120482511</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Irving+Kaplansky&rft.btitle=More+Mathematical+People&rft.pages=118-136&rft.pub=Harcourt+Brace+Jovanovich&rft.date=1990&rft.isbn=9780120482511&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DNu_uAAAAMAAJ&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIrving+Kaplansky" 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="CITEREFDavidson2006" class="citation web cs1">Davidson, Keay (2006-07-02). <a rel="nofollow" class="external text" href="https://www.sfgate.com/bayarea/article/Irving-Kaplansky-mathematician-and-author-2532313.php">"Irving Kaplansky -- mathematician and author"</a>. <i>SFGATE</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2022-10-07</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=SFGATE&rft.atitle=Irving+Kaplansky+--+mathematician+and+author&rft.date=2006-07-02&rft.aulast=Davidson&rft.aufirst=Keay&rft_id=https%3A%2F%2Fwww.sfgate.com%2Fbayarea%2Farticle%2FIrving-Kaplansky-mathematician-and-author-2532313.php&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIrving+Kaplansky" 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"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20140106040941/http://senate.universityofcalifornia.edu/inmemoriam/irvingkaplansky.html">"In memoriam: Irving Kaplansky"</a>. Archived from <a rel="nofollow" class="external text" href="http://senate.universityofcalifornia.edu/inmemoriam/irvingkaplansky.html">the original</a> on 2014-01-06<span class="reference-accessdate">. Retrieved <span class="nowrap">2014-01-05</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=In+memoriam%3A+Irving+Kaplansky&rft_id=http%3A%2F%2Fsenate.universityofcalifornia.edu%2Finmemoriam%2Firvingkaplansky.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIrving+Kaplansky" class="Z3988"></span></span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.ancestry.com/sharing/13714616?h=b1f78e">"Irving Kaplansky discovered in Canada, Selected School Yearbooks, 1901-2010"</a>. <i>Ancestry.com</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2022-10-07</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Ancestry.com&rft.atitle=Irving+Kaplansky+discovered+in+Canada%2C+Selected+School+Yearbooks%2C+1901-2010&rft_id=https%3A%2F%2Fwww.ancestry.com%2Fsharing%2F13714616%3Fh%3Db1f78e&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIrving+Kaplansky" class="Z3988"></span></span> </li> <li id="cite_note-d.umn.edu-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-d.umn.edu_9-0">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://www.d.umn.edu/~jgallian/putnam15.pdf">The Putnam Competition from 1938-2015 by Joseph A. Gallian</a></span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text">MacLane, Saunders. "The Applied Mathematics Group at Columbia in World War II" in <i>A Century of Mathematics in America</i>, vol. 3 (ed. Peter Duren). Providence: American Mathematical Society, 1989.</span> </li> <li id="cite_note-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-11">^</a></b></span> <span class="reference-text">Defense Technical Information Center. <a rel="nofollow" class="external free" href="http://www.dtic.mil/dtic/tr/fulltext/u2/b809137.pdf">http://www.dtic.mil/dtic/tr/fulltext/u2/b809137.pdf</a></span> </li> <li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text">Kaplansky, Irving. "Abraham Adrian Albert" 1972. <a rel="nofollow" class="external free" href="http://www.ams.org/samplings/math-history/hmath1-kaplansky17.pdf">http://www.ams.org/samplings/math-history/hmath1-kaplansky17.pdf</a></span> </li> <li id="cite_note-ReferenceA-13"><span class="mw-cite-backlink">^ <a href="#cite_ref-ReferenceA_13-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-ReferenceA_13-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://mathshistory.st-andrews.ac.uk/Biographies/Kaplansky/">"Irving Kaplansky - Biography"</a>. <i>Maths History</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2022-10-07</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Maths+History&rft.atitle=Irving+Kaplansky+-+Biography&rft_id=https%3A%2F%2Fmathshistory.st-andrews.ac.uk%2FBiographies%2FKaplansky%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIrving+Kaplansky" class="Z3988"></span></span> </li> <li id="cite_note-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-14">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.ias.edu/scholars/irving-kaplansky">"Irving Kaplansky - Scholars | Institute for Advanced Study"</a>. 9 December 2019.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Irving+Kaplansky+-+Scholars+%26%23124%3B+Institute+for+Advanced+Study&rft.date=2019-12-09&rft_id=https%3A%2F%2Fwww.ias.edu%2Fscholars%2Firving-kaplansky&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIrving+Kaplansky" class="Z3988"></span></span> </li> <li id="cite_note-ams.org-15"><span class="mw-cite-backlink">^ <a href="#cite_ref-ams.org_15-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-ams.org_15-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text">Bass, Hyman and Lam, T.Y., (December, 2007) "Irving Kaplansky (1917-2007)." Notices of the American Mathematical Society. (54)11,1477-1493. <a rel="nofollow" class="external free" href="http://www.ams.org/notices/200711/tx071101477p.pdf">http://www.ams.org/notices/200711/tx071101477p.pdf</a></span> </li> <li id="cite_note-16"><span class="mw-cite-backlink"><b><a href="#cite_ref-16">^</a></b></span> <span class="reference-text">Kaplansky, I. (1967). Mathematics. In: Book of the Year: Events of 1966, 9th ed. Chicago, Toronto, London, Geneva, Sydney, Tokyo, Manila: William Benton, pp.502-503.</span> </li> <li id="cite_note-17"><span class="mw-cite-backlink"><b><a href="#cite_ref-17">^</a></b></span> <span class="reference-text">Kaplansky, I. (1968). Mathematics. In: Book of the Year: Events of 1967, 9th ed. Chicago, Toronto, London, Geneva, Sydney, Tokyo, Manila: William Benton, pp.502.</span> </li> <li id="cite_note-18"><span class="mw-cite-backlink"><b><a href="#cite_ref-18">^</a></b></span> <span class="reference-text">Kaplansky, I. (1969). Mathematics. In: Book of the Year: Events of 1968, 9th ed. Chicago, Toronto, London, Geneva, Sydney, Tokyo, Manila: William Benton, pp.488-489.</span> </li> <li id="cite_note-19"><span class="mw-cite-backlink"><b><a href="#cite_ref-19">^</a></b></span> <span class="reference-text"><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/Kaplansky.html">"Irving Kaplansky"</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=Irving+Kaplansky&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%2FKaplansky.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIrving+Kaplansky" class="Z3988"></span></span> </li> <li id="cite_note-20"><span class="mw-cite-backlink"><b><a href="#cite_ref-20">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFTourist2013" class="citation web cs1">Tourist, Math (2013-09-22). <a rel="nofollow" class="external text" href="http://mtarchive.blogspot.com/2013/09/a-song-about-pi.html">"MTArchive: A Song about Pi"</a>. <i>MTArchive</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2022-10-07</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=MTArchive&rft.atitle=MTArchive%3A+A+Song+about+Pi&rft.date=2013-09-22&rft.aulast=Tourist&rft.aufirst=Math&rft_id=http%3A%2F%2Fmtarchive.blogspot.com%2F2013%2F09%2Fa-song-about-pi.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIrving+Kaplansky" class="Z3988"></span></span> </li> <li id="cite_note-21"><span class="mw-cite-backlink"><b><a href="#cite_ref-21">^</a></b></span> <span class="reference-text">Pearce, Jeremy "Irving Kaplansky, 89, a Pioneer in Mathematical Exploration" <a rel="nofollow" class="external free" href="https://www.nytimes.com/2006/07/13/us/13kaplansky.html_r=1&oref=slogin">https://www.nytimes.com/2006/07/13/us/13kaplansky.html_r=1&oref=slogin</a></span> </li> <li id="cite_note-22"><span class="mw-cite-backlink"><b><a href="#cite_ref-22">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBaer,_Reinhold1955" class="citation journal cs1"><a href="/wiki/Reinhold_Baer" title="Reinhold Baer">Baer, Reinhold</a> (1955). <a rel="nofollow" class="external text" href="https://www.ams.org/journals/bull/1955-61-01/S0002-9904-1955-09877-X/S0002-9904-1955-09877-X.pdf">"Review: <i>Infinite abelian groups</i> by I. Kaplansky"</a> <span class="cs1-format">(PDF)</span>. <i>Bull. Amer. Math. Soc</i>. <b>61</b> (1): 88–89. <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%2Fs0002-9904-1955-09877-x">10.1090/s0002-9904-1955-09877-x</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Bull.+Amer.+Math.+Soc.&rft.atitle=Review%3A+Infinite+abelian+groups+by+I.+Kaplansky&rft.volume=61&rft.issue=1&rft.pages=88-89&rft.date=1955&rft_id=info%3Adoi%2F10.1090%2Fs0002-9904-1955-09877-x&rft.au=Baer%2C+Reinhold&rft_id=https%3A%2F%2Fwww.ams.org%2Fjournals%2Fbull%2F1955-61-01%2FS0002-9904-1955-09877-X%2FS0002-9904-1955-09877-X.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIrving+Kaplansky" class="Z3988"></span></span> </li> </ol></div> <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=Irving_Kaplansky&action=edit&section=9" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAlbert,_Nancy_E.2007" class="citation journal cs1">Albert, Nancy E. (2007). <a rel="nofollow" class="external text" href="http://celebratio.org/Kaplansky_I/article/399/">"Irving Kaplansky: Some Reflections on His Early Years"</a> <span class="cs1-format">(<a href="/wiki/PDF" title="PDF">PDF</a>)</span><span class="reference-accessdate">. Retrieved <span class="nowrap">2008-06-27</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Irving+Kaplansky%3A+Some+Reflections+on+His+Early+Years&rft.date=2007&rft.au=Albert%2C+Nancy+E.&rft_id=http%3A%2F%2Fcelebratio.org%2FKaplansky_I%2Farticle%2F399%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIrving+Kaplansky" class="Z3988"></span> <span class="cs1-visible-error citation-comment"><code class="cs1-code">{{<a href="/wiki/Template:Cite_journal" title="Template:Cite journal">cite journal</a>}}</code>: </span><span class="cs1-visible-error citation-comment">Cite journal requires <code class="cs1-code">|journal=</code> (<a href="/wiki/Help:CS1_errors#missing_periodical" title="Help:CS1 errors">help</a>)</span></li> <li>Peterson, Ivars. (2013). "A Song about Pi" <a rel="nofollow" class="external free" href="http://mtarchive.blogspot.com/2013/09/a-song-about-pi.html?m=1">http://mtarchive.blogspot.com/2013/09/a-song-about-pi.html?m=1</a></li> <li>Freund, Peter G. O. <i>Irving Kaplansky and Supersymmetry</i>. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<a rel="nofollow" class="external text" href="https://arxiv.org/abs/physics/0703037">physics/0703037</a></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBassLam,_T.Y.2007" class="citation journal cs1"><a href="/wiki/Hyman_Bass" title="Hyman Bass">Bass, Hyman</a>; <a href="/wiki/Tsit_Yuen_Lam" title="Tsit Yuen Lam">Lam, T.Y.</a> (December 2007). <a rel="nofollow" class="external text" href="https://www.ams.org/notices/200711/tx071101477p.pdf">"Irving Kaplansky (1917–2006)"</a> <span class="cs1-format">(PDF)</span>. <i><a href="/wiki/Notices_of_the_American_Mathematical_Society" title="Notices of the American Mathematical Society">Notices of the American Mathematical Society</a></i>. <b>54</b> (11): 1477–1493<span class="reference-accessdate">. Retrieved <span class="nowrap">2008-01-05</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Notices+of+the+American+Mathematical+Society&rft.atitle=Irving+Kaplansky+%281917%26ndash%3B2006%29&rft.volume=54&rft.issue=11&rft.pages=1477-1493&rft.date=2007-12&rft.aulast=Bass&rft.aufirst=Hyman&rft.au=Lam%2C+T.Y.&rft_id=https%3A%2F%2Fwww.ams.org%2Fnotices%2F200711%2Ftx071101477p.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIrving+Kaplansky" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKadison2008" class="citation journal cs1"><a href="/wiki/Richard_V._Kadison" class="mw-redirect" title="Richard V. Kadison">Kadison, Richard V.</a> (February 2008). <a rel="nofollow" class="external text" href="https://www.ams.org/notices/200802/tx080200216p.pdf">"Irving Kaplansky's Role in Mid-Twentieth Century Functional Analysis"</a> <span class="cs1-format">(PDF)</span>. <i>Notices of the AMS</i>. <b>55</b> (2): 216–225<span class="reference-accessdate">. Retrieved <span class="nowrap">2008-01-05</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Notices+of+the+AMS&rft.atitle=Irving+Kaplansky%27s+Role+in+Mid-Twentieth+Century+Functional+Analysis&rft.volume=55&rft.issue=2&rft.pages=216-225&rft.date=2008-02&rft.aulast=Kadison&rft.aufirst=Richard+V.&rft_id=https%3A%2F%2Fwww.ams.org%2Fnotices%2F200802%2Ftx080200216p.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIrving+Kaplansky" class="Z3988"></span></li></ul> <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=Irving_Kaplansky&action=edit&section=10" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><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/Kaplansky.html">"Irving Kaplansky"</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=Irving+Kaplansky&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%2FKaplansky.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIrving+Kaplansky" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPearce2006" class="citation news cs1">Pearce, Jeremy (July 13, 2006). <a rel="nofollow" class="external text" href="https://www.nytimes.com/2006/07/13/us/13kaplansky.html?_r=1&oref=slogin">"Irving Kaplansky, 89, a Pioneer in Mathematical Exploration"</a>. <i><a href="/wiki/The_New_York_Times" title="The New York Times">The New York Times</a></i>. p. C15<span class="reference-accessdate">. Retrieved <span class="nowrap">2008-01-05</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+New+York+Times&rft.atitle=Irving+Kaplansky%2C+89%2C+a+Pioneer+in+Mathematical+Exploration&rft.pages=C15&rft.date=2006-07-13&rft.aulast=Pearce&rft.aufirst=Jeremy&rft_id=https%3A%2F%2Fwww.nytimes.com%2F2006%2F07%2F13%2Fus%2F13kaplansky.html%3F_r%3D1%26oref%3Dslogin&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIrving+Kaplansky" class="Z3988"></span></li> <li><a rel="nofollow" class="external text" href="http://zakuski.math.utsa.edu/~kap/">Irving Kaplansky + Ternary Quadratic Forms</a></li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20100618052056/http://zakuski.math.utsa.edu/~kap/superalgebra.html">Irving Kaplansky + Lie Superalgebras</a></li> <li><a rel="nofollow" class="external text" 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Kaplansky album)">Every Single Day</a></i> (2001)</li> <li><i><a href="/wiki/The_Red_Thread_(Lucy_Kaplansky_album)" title="The Red Thread (Lucy Kaplansky album)">The Red Thread</a></i> (2004)</li> <li><i><a href="/wiki/Over_the_Hills" title="Over the Hills">Over the Hills</a></i> (2007)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Collaboration albums</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><i><a href="/wiki/Cry_Cry_Cry" title="Cry Cry Cry">Cry Cry Cry</a></i> (1998)</li> <li><i><a href="/wiki/Red_Horse_(album)" title="Red Horse (album)">Red Horse</a></i> (2010)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Related articles</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Eliza_Gilkyson" title="Eliza Gilkyson">Eliza Gilkyson</a></li> <li><a class="mw-selflink selflink">Irving Kaplansky</a></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="Presidents_of_the_American_Mathematical_Society" style="padding:3px"><table class="nowraplinks mw-collapsible mw-collapsed navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:AMS_Presidents" title="Template:AMS Presidents"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:AMS_Presidents" title="Template talk:AMS Presidents"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:AMS_Presidents" title="Special:EditPage/Template:AMS Presidents"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Presidents_of_the_American_Mathematical_Society" style="font-size:114%;margin:0 4em">Presidents of the <a href="/wiki/American_Mathematical_Society" title="American Mathematical Society">American Mathematical Society</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">1888–1900</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><span class="nowrap"><a href="/wiki/John_Howard_Van_Amringe" title="John Howard Van Amringe">John Howard Van Amringe</a> (1888–1890)</span></li> <li><span class="nowrap"><a href="/wiki/Emory_McClintock" title="Emory McClintock">Emory McClintock</a> (1891–1894)</span></li> <li><span class="nowrap"><a href="/wiki/George_William_Hill" title="George William Hill">George William Hill</a> (1895–1896)</span></li> <li><span class="nowrap"><a href="/wiki/Simon_Newcomb" title="Simon Newcomb">Simon Newcomb</a> (1897–1898)</span></li> <li><span class="nowrap"><a href="/wiki/Robert_Simpson_Woodward" title="Robert Simpson Woodward">Robert Simpson Woodward</a> (1899–1900)</span></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">1901–1924</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><span class="nowrap"><a href="/wiki/E._H._Moore" title="E. H. Moore">E. H. Moore</a> (1901–1902)</span></li> <li><span class="nowrap"><a href="/wiki/Thomas_Fiske" title="Thomas Fiske">Thomas Fiske</a> (1903–1904)</span></li> <li><span class="nowrap"><a href="/wiki/William_Fogg_Osgood" title="William Fogg Osgood">William Fogg Osgood</a> (1905–1906)</span></li> <li><span class="nowrap"><a href="/wiki/Henry_Seely_White" title="Henry Seely White">Henry Seely White</a> (1907–1908)</span></li> <li><span class="nowrap"><a href="/wiki/Maxime_B%C3%B4cher" title="Maxime Bôcher">Maxime Bôcher</a> (1909–1910)</span></li> <li><span class="nowrap"><a href="/wiki/Henry_Burchard_Fine" title="Henry Burchard Fine">Henry Burchard Fine</a> (1911–1912)</span></li> <li><span class="nowrap"><a href="/wiki/Edward_Burr_Van_Vleck" title="Edward Burr Van Vleck">Edward Burr Van Vleck</a> (1913–1914)</span></li> <li><span class="nowrap"><a href="/wiki/Ernest_William_Brown" title="Ernest William Brown">Ernest William Brown</a> (1915–1916)</span></li> <li><span class="nowrap"><a href="/wiki/Leonard_Eugene_Dickson" title="Leonard Eugene Dickson">Leonard Eugene Dickson</a> (1917–1918)</span></li> <li><span class="nowrap"><a href="/wiki/Frank_Morley" title="Frank Morley">Frank Morley</a> (1919–1920)</span></li> <li><span class="nowrap"><a href="/wiki/Gilbert_Ames_Bliss" title="Gilbert Ames Bliss">Gilbert Ames Bliss</a> (1921–1922)</span></li> <li><span class="nowrap"><a href="/wiki/Oswald_Veblen" title="Oswald Veblen">Oswald Veblen</a> (1923–1924)</span></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">1925–1950</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><span class="nowrap"><a href="/wiki/George_David_Birkhoff" title="George David Birkhoff">George David Birkhoff</a> (1925–1926)</span></li> <li><span class="nowrap"><a href="/wiki/Virgil_Snyder" title="Virgil Snyder">Virgil Snyder</a> (1927–1928)</span></li> <li><span class="nowrap"><a href="/wiki/Earle_Raymond_Hedrick" title="Earle Raymond Hedrick">Earle Raymond Hedrick</a> (1929–1930)</span></li> <li><span class="nowrap"><a href="/wiki/Luther_P._Eisenhart" title="Luther P. Eisenhart">Luther P. Eisenhart</a> (1931–1932)</span></li> <li><span class="nowrap"><a href="/wiki/Arthur_Byron_Coble" title="Arthur Byron Coble">Arthur Byron Coble</a> (1933–1934)</span></li> <li><span class="nowrap"><a href="/wiki/Solomon_Lefschetz" title="Solomon Lefschetz">Solomon Lefschetz</a> (1935–1936)</span></li> <li><span class="nowrap"><a href="/wiki/Robert_Lee_Moore" title="Robert Lee Moore">Robert Lee Moore</a> (1937–1938)</span></li> <li><span class="nowrap"><a href="/wiki/Griffith_C._Evans" title="Griffith C. Evans">Griffith C. Evans</a> (1939–1940)</span></li> <li><span class="nowrap"><a href="/wiki/Marston_Morse" title="Marston Morse">Marston Morse</a> (1941–1942)</span></li> <li><span class="nowrap"><a href="/wiki/Marshall_H._Stone" title="Marshall H. Stone">Marshall H. Stone</a> (1943–1944)</span></li> <li><span class="nowrap"><a href="/wiki/Theophil_Henry_Hildebrandt" title="Theophil Henry Hildebrandt">Theophil Henry Hildebrandt</a> (1945–1946)</span></li> <li><span class="nowrap"><a href="/wiki/Einar_Hille" title="Einar Hille">Einar Hille</a> (1947–1948)</span></li> <li><span class="nowrap"><a href="/wiki/Joseph_L._Walsh" title="Joseph L. Walsh">Joseph L. Walsh</a> (1949–1950)</span></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">1951–1974</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><span class="nowrap"><a href="/wiki/John_von_Neumann" title="John von Neumann">John von Neumann</a> (1951–1952)</span></li> <li><span class="nowrap"><a href="/wiki/Gordon_Thomas_Whyburn" class="mw-redirect" title="Gordon Thomas Whyburn">Gordon Thomas Whyburn</a> (1953–1954)</span></li> <li><span class="nowrap"><a href="/wiki/Raymond_Louis_Wilder" title="Raymond Louis Wilder">Raymond Louis Wilder</a> (1955–1956)</span></li> <li><span class="nowrap"><a href="/wiki/Richard_Brauer" title="Richard Brauer">Richard Brauer</a> (1957–1958)</span></li> <li><span class="nowrap"><a href="/wiki/Edward_J._McShane" title="Edward J. McShane">Edward J. McShane</a> (1959–1960)</span></li> <li><span class="nowrap"><a href="/wiki/Deane_Montgomery" title="Deane Montgomery">Deane Montgomery</a> (1961–1962)</span></li> <li><span class="nowrap"><a href="/wiki/Joseph_L._Doob" title="Joseph L. Doob">Joseph L. Doob</a> (1963–1964)</span></li> <li><span class="nowrap"><a href="/wiki/Abraham_Adrian_Albert" class="mw-redirect" title="Abraham Adrian Albert">Abraham Adrian Albert</a> (1965–1966)</span></li> <li><span class="nowrap"><a href="/wiki/Charles_B._Morrey_Jr." title="Charles B. Morrey Jr.">Charles B. Morrey Jr.</a> (1967–1968)</span></li> <li><span class="nowrap"><a href="/wiki/Oscar_Zariski" title="Oscar Zariski">Oscar Zariski</a> (1969–1970)</span></li> <li><span class="nowrap"><a href="/wiki/Nathan_Jacobson" title="Nathan Jacobson">Nathan Jacobson</a> (1971–1972)</span></li> <li><span class="nowrap"><a href="/wiki/Saunders_Mac_Lane" title="Saunders Mac Lane">Saunders Mac Lane</a> (1973–1974)</span></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">1975–2000</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><span class="nowrap"><a href="/wiki/Lipman_Bers" title="Lipman Bers">Lipman Bers</a> (1975–1976)</span></li> <li><span class="nowrap"><a href="/wiki/R._H._Bing" title="R. H. Bing">R. H. Bing</a> (1977–1978)</span></li> <li><span class="nowrap"><a href="/wiki/Peter_Lax" title="Peter Lax">Peter Lax</a> (1979–1980)</span></li> <li><span class="nowrap"><a href="/wiki/Andrew_M._Gleason" title="Andrew M. Gleason">Andrew M. Gleason</a> (1981–1982)</span></li> <li><span class="nowrap"><a href="/wiki/Julia_Robinson" title="Julia Robinson">Julia Robinson</a> (1983–1984)</span></li> <li><span class="nowrap"><a class="mw-selflink selflink">Irving Kaplansky</a> (1985–1986)</span></li> <li><span class="nowrap"><a href="/wiki/George_Mostow" title="George Mostow">George Mostow</a> (1987–1988)</span></li> <li><span class="nowrap"><a href="/wiki/William_Browder_(mathematician)" title="William Browder (mathematician)">William Browder</a> (1989–1990)</span></li> <li><span class="nowrap"><a href="/wiki/Michael_Artin" title="Michael Artin">Michael Artin</a> (1991–1992)</span></li> <li><span class="nowrap"><a href="/wiki/Ronald_Graham" title="Ronald Graham">Ronald Graham</a> (1993–1994)</span></li> <li><span class="nowrap"><a href="/wiki/Cathleen_Synge_Morawetz" title="Cathleen Synge Morawetz">Cathleen Synge Morawetz</a> (1995–1996)</span></li> <li><span class="nowrap"><a href="/wiki/Arthur_Jaffe" title="Arthur Jaffe">Arthur Jaffe</a> (1997–1998)</span></li> <li><span class="nowrap"><a href="/wiki/Felix_Browder" title="Felix Browder">Felix Browder</a> (1999–2000)</span></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">2001–2024</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><span class="nowrap"><a href="/wiki/Hyman_Bass" title="Hyman Bass">Hyman Bass</a> (2001–2002)</span></li> <li><span class="nowrap"><a href="/wiki/David_Eisenbud" title="David Eisenbud">David Eisenbud</a> (2003–2004)</span></li> <li><span class="nowrap"><a href="/wiki/James_Arthur_(mathematician)" title="James Arthur (mathematician)">James Arthur</a> (2005–2006)</span></li> <li><span class="nowrap"><a href="/wiki/James_Glimm" title="James Glimm">James Glimm</a> (2007–2008)</span></li> <li><span class="nowrap"><a href="/wiki/George_Andrews_(mathematician)" title="George Andrews (mathematician)">George Andrews</a> (2009–2010)</span></li> <li><span class="nowrap"><a href="/wiki/Eric_Friedlander" title="Eric Friedlander">Eric Friedlander</a> (2011–2012)</span></li> <li><span class="nowrap"><a href="/wiki/David_Vogan" title="David Vogan">David Vogan</a> (2013–2014)</span></li> <li><span class="nowrap"><a href="/wiki/Robert_Bryant_(mathematician)" title="Robert Bryant (mathematician)">Robert Bryant</a> (2015–2016)</span></li> <li><span class="nowrap"><a href="/wiki/Ken_Ribet" title="Ken Ribet">Ken Ribet</a> (2017–2018)</span></li> <li><span class="nowrap"><a href="/wiki/Jill_Pipher" title="Jill Pipher">Jill Pipher</a> (2019–2020)</span></li> <li><span class="nowrap"><a href="/wiki/Ruth_Charney" title="Ruth Charney">Ruth Charney</a> (2021–2022)</span></li> <li><span class="nowrap"><a href="/wiki/Bryna_Kra" title="Bryna Kra">Bryna Kra</a> (2023–2024)</span></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"><style data-mw-deduplicate="TemplateStyles:r1038841319">.mw-parser-output .tooltip-dotted{border-bottom:1px dotted;cursor:help}</style></div><div role="navigation" class="navbox authority-control" aria-labelledby="Authority_control_databases_frameless&#124;text-top&#124;10px&#124;alt=Edit_this_at_Wikidata&#124;link=https&#58;//www.wikidata.org/wiki/Q129368#identifiers&#124;class=noprint&#124;Edit_this_at_Wikidata" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Authority_control_databases_frameless&#124;text-top&#124;10px&#124;alt=Edit_this_at_Wikidata&#124;link=https&#58;//www.wikidata.org/wiki/Q129368#identifiers&#124;class=noprint&#124;Edit_this_at_Wikidata" style="font-size:114%;margin:0 4em"><a href="/wiki/Help:Authority_control" title="Help:Authority control">Authority control databases</a> <span class="mw-valign-text-top noprint" typeof="mw:File/Frameless"><a href="https://www.wikidata.org/wiki/Q129368#identifiers" title="Edit this at Wikidata"><img alt="Edit this at Wikidata" src="//upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/10px-OOjs_UI_icon_edit-ltr-progressive.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/15px-OOjs_UI_icon_edit-ltr-progressive.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/20px-OOjs_UI_icon_edit-ltr-progressive.svg.png 2x" data-file-width="20" data-file-height="20" /></a></span></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">International</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://isni.org/isni/0000000110323223">ISNI</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://viaf.org/viaf/108934540">VIAF</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://id.oclc.org/worldcat/entity/E39PBJhMmq8FPCJqWdpCgt6Frq">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/119264358">Germany</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://id.loc.gov/authorities/n79056726">United States</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://catalogue.bnf.fr/ark:/12148/cb11909416h">France</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://data.bnf.fr/ark:/12148/cb11909416h">BnF data</a></span></li><li><span class="uid"><span class="rt-commentedText tooltip tooltip-dotted" title="Kaplansky, Irving"><a rel="nofollow" class="external text" href="https://opac.sbn.it/nome/MILV013685">Italy</a></span></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://aleph.nkp.cz/F/?func=find-c&local_base=aut&ccl_term=ica=jx20061125003&CON_LNG=ENG">Czech Republic</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="http://data.bibliotheken.nl/id/thes/p068408153">Netherlands</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://authority.bibsys.no/authority/rest/authorities/html/90264977">Norway</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://kopkatalogs.lv/F?func=direct&local_base=lnc10&doc_number=000167723&P_CON_LNG=ENG">Latvia</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://libris.kb.se/mkz29rp518dbvpb">Sweden</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://dbn.bn.org.pl/descriptor-details/9810538023105606">Poland</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="http://olduli.nli.org.il/F/?func=find-b&local_base=NLX10&find_code=UID&request=987007460676105171">Israel</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://cantic.bnc.cat/registre/981058513033506706">Catalonia</a></span></li></ul></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Academics</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://www.mathgenealogy.org/id.php?id=833">Mathematics Genealogy Project</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://www.scopus.com/authid/detail.uri?authorId=6602323921">Scopus</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://zbmath.org/authors/?q=ai:kaplansky.irving">zbMATH</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://dblp.org/pid/129/8726">DBLP</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://mathscinet.ams.org/mathscinet/MRAuthorID/98080">MathSciNet</a></span></li></ul></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">People</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://www.deutsche-biographie.de/pnd119264358.html?language=en">Deutsche Biographie</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://www.deutsche-digitale-bibliothek.de/person/gnd/119264358">DDB</a></span></li></ul></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://www.idref.fr/02694538X">IdRef</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://snaccooperative.org/ark:/99166/w6md0rb4">SNAC</a></span></li></ul></div></td></tr></tbody></table></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" 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