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Canadian mathematician (1917–2006)
Irving Kaplansky (March 22, 1917 – June 25, 2006) was a mathematician, college professor, author, and amateur musician. Kaplansky, or "Kap" as his friends
Irving_Kaplansky
Numerous conjectures by mathematician Irving Kaplansky
The mathematician Irving Kaplansky is notable for proposing numerous conjectures in several branches of mathematics, including a list of ten conjectures
Kaplansky's_conjectures
American folk musician
guitar, mandolin, and piano. Kaplansky was originally from Chicago; her father was the noted mathematician Irving Kaplansky (1917–2006). Later, she would
Lucy_Kaplansky
Surname list
activist Irving Kaplansky (1917–2006), Canadian mathematician Lucy Kaplansky (born 1960), an American folk musician, daughter of Irving Kaplansky Shlomo
Kapłański
In the theory of von Neumann algebras, the Kaplansky density theorem, due to Irving Kaplansky, is a fundamental approximation theorem. The importance and
Kaplansky_density_theorem
Abstract board game for two players
not have any stones of the opposite color on it. It is named after Irving Kaplansky. k ≤ 3 is a first-player win. 4 ≤ k ≤ 7 is believed to be draw, but
Kaplansky's_game
Result on simultaneous representation of primes by quadratic forms
mathematics, Kaplansky's theorem on quadratic forms is a result on simultaneous representation of primes by quadratic forms. It was proved in 2003 by Irving Kaplansky
Kaplansky's theorem on quadratic forms
Kaplansky's_theorem_on_quadratic_forms
American mathematician
titled Global dimensions of rings, was written under the supervision of Irving Kaplansky. He has held visiting appointments at the Institute for Advanced Study
Hyman_Bass
Name list
official) Irving Kaplan (chemist) (1913–1997), American chemist Irving Kaplan (radiation oncologist), American radiation oncologist Irving Kaplansky (1917–2006)
Irving_(name)
On the dimension of vector space duals
dimension of any function space. The theorem is named after Paul Erdős and Irving Kaplansky. Let E {\displaystyle E} be an infinite-dimensional vector space over
Erdős–Kaplansky_theorem
In abstract algebra, Kaplansky's theorem on projective modules, first proven by Irving Kaplansky, states that a projective module over a local ring is
Kaplansky's theorem on projective modules
Kaplansky's_theorem_on_projective_modules
American mathematician
Ph.D. from the University of Chicago in 1957 under the guidance of Irving Kaplansky. During his career at Stanford University he supervised the Ph. D.
Donald_Samuel_Ornstein
German-born mathematician (1929–2005)
Chicago, he completed a doctorate in 1959 under the supervision of Irving Kaplansky. Following short-term positions at the University of California, Los
Günter_Lumer
algebraic generalization of a W*-algebra. They were introduced by Irving Kaplansky in 1951. As operator algebras, von Neumann algebras, among all C*-algebras
AW*-algebra
American mathematician (1917–1955)
going-up and going-down theorems. He also coauthored articles with Irving Kaplansky. One of his doctoral students was R. Duncan Luce. Cohen died unexpectedly
Irvin_Cohen
Mathematical objects that generalise the notion of Hilbert spaces
introduced in the work of Irving Kaplansky in 1953, which developed the theory for commutative, unital algebras (though Kaplansky observed that the assumption
Hilbert_C*-module
American musician (1928–2025)
of 15 he entered Harvard College, where one of his professors was Irving Kaplansky. As an undergraduate student at Harvard, he began to write comic songs
Tom_Lehrer
American mathematician (1905–1972)
Nelson Cole Prizes in algebra and number theory (43% of recipients) Kaplansky, Irving. "Abraham Adrian Albert: 1905–1972". Celebratio Mathematica. Mathematical
A._A._Albert
Mathematical counting-out question
considerably from source to source. For instance, Israel Nathan Herstein and Irving Kaplansky (1974) have Josephus and 39 comrades stand in a circle with every seventh
Josephus_problem
American mathematician (born 1943)
where she completed her doctorate in 1968 under the supervision of Irving Kaplansky. She taught at Boston University and at the University of Illinois
Susanna_S._Epp
Mathematician (1934–2016)
1959 with a thesis in abelian groups written under the direction of Irving Kaplansky. In 1959 he moved to the University of Illinois at Urbana–Champaign
Joseph_J._Rotman
American mathematician (1937–2024)
thesis "Regular Overrings of Regular Local Rings" was supervised by Irving Kaplansky. Sally was an accomplished runner, completing several Chicago Marathons
Judith_D._Sally
American mathematician
(1979–1980) Andrew M. Gleason (1981–1982) Julia Robinson (1983–1984) Irving Kaplansky (1985–1986) George Mostow (1987–1988) William Browder (1989–1990) Michael
R._H._Bing
American mathematician (1909–2005)
he published his first scientific paper, in physics and co-authored with Irving Langmuir. In 1929, at a party of Yale football supporters in Montclair,
Saunders_Mac_Lane
radical can be lifted to R. The abbreviation SBI was introduced by Irving Kaplansky and stands for "suitable for building idempotent elements". Any ring
SBI_ring
American mathematician (born 1934)
(1979–1980) Andrew M. Gleason (1981–1982) Julia Robinson (1983–1984) Irving Kaplansky (1985–1986) George Mostow (1987–1988) William Browder (1989–1990) Michael
Michael_Artin
Russian-born American mathematician (1884–1972)
(1979–1980) Andrew M. Gleason (1981–1982) Julia Robinson (1983–1984) Irving Kaplansky (1985–1986) George Mostow (1987–1988) William Browder (1989–1990) Michael
Solomon_Lefschetz
American mathematician (1923–2015)
Matlis earned his Ph.D. at the University of Chicago in 1958, with Irving Kaplansky as advisor. He is an emeritus professor at Northwestern University
Eben_Matlis
American mathematician (1919–1985)
(1979–1980) Andrew M. Gleason (1981–1982) Julia Robinson (1983–1984) Irving Kaplansky (1985–1986) George Mostow (1987–1988) William Browder (1989–1990) Michael
Julia_Robinson
American mathematician (1910–2004)
(1979–1980) Andrew M. Gleason (1981–1982) Julia Robinson (1983–1984) Irving Kaplansky (1985–1986) George Mostow (1987–1988) William Browder (1989–1990) Michael
Joseph_L._Doob
American mathematician
(1979–1980) Andrew M. Gleason (1981–1982) Julia Robinson (1983–1984) Irving Kaplansky (1985–1986) George Mostow (1987–1988) William Browder (1989–1990) Michael
Marshall_H._Stone
Croatian-born NASA engineer (1947–2012)
mathematics from the University of Chicago under the supervision of Irving Kaplansky. In 1981, Matijevic began working at the Jet Propulsion Laboratory
Jacob_Matijevic
(1933– ), computer scientist and mathematician; Turing Award (1989) Irving Kaplansky (1917–2006), mathematician Yael Karshon (1964– ), symplectic geometer[citation
List_of_Canadian_Jews
The axioms for complex Jordan operator algebras, first suggested by Irving Kaplansky in 1976, require an involution and are called JB* algebras or Jordan
Jordan_operator_algebra
Academic department at the University of Toronto
Canada. The Department's competitive mathematics team, consisting of Irving Kaplansky, Nathan Mendelsohn and John Coleman, won first place in the first year
Department of Mathematics (University of Toronto)
Department_of_Mathematics_(University_of_Toronto)
infinite-dimensional C*-algebras with this property exist was posed in 1958 by Irving Kaplansky, and the first example of one was published in 1981 by Bruce Blackadar
Projectionless_C*-algebra
American mathematician (1895–1973)
(1979–1980) Andrew M. Gleason (1981–1982) Julia Robinson (1983–1984) Irving Kaplansky (1985–1986) George Mostow (1987–1988) William Browder (1989–1990) Michael
Joseph_L._Walsh
Puerto Rican mathematician
(1979–1980) Andrew M. Gleason (1981–1982) Julia Robinson (1983–1984) Irving Kaplansky (1985–1986) George Mostow (1987–1988) William Browder (1989–1990) Michael
Eric_Friedlander
conjecture, counterexample announced 2019 Hirsch conjecture (disproved 2010) Kaplansky unit conjecture Intersection graph conjecture Kelvin's conjecture Kouchnirenko's
List_of_conjectures
First article on transfinite set theory
is fundamentally constructive and not merely existential." In 1972, Irving Kaplansky wrote: "It is often said that Cantor's proof is not 'constructive,'
Cantor's first set theory article
Cantor's_first_set_theory_article
German mathematician (1882–1935)
the Lasker–Noether theorem in its full generality. Noted algebraist Irving Kaplansky called this work "revolutionary". The publication gave rise to the
Emmy_Noether
(1912–1986), mathematician and economist; Nobel Prize in Economics (1975) Irving Kaplansky (1917–2006), mathematician Samuel Karlin (1924–2007), mathematician
List_of_Jewish_mathematicians
theory of elementary divisors to infinite matrices. George Mackey and Irving Kaplansky generalized Ulm's theorem to certain modules over a complete discrete
Height_(abelian_group)
(Mathematical) ring with a unique maximal ideal
ring R/J is again local, with maximal ideal m/J. A deep theorem by Irving Kaplansky says that any projective module over a local ring is free, though the
Local_ring
Hungarian and American mathematician and physicist (1903–1957)
basis for further investigations of algebraic quantum mechanics started by Irving Segal. Von Neumann was the first to establish a rigorous mathematical framework
John_von_Neumann
American mathematician (born 1938)
(1979–1980) Andrew M. Gleason (1981–1982) Julia Robinson (1983–1984) Irving Kaplansky (1985–1986) George Mostow (1987–1988) William Browder (1989–1990) Michael
George Andrews (mathematician)
George_Andrews_(mathematician)
American mathematician
(1979–1980) Andrew M. Gleason (1981–1982) Julia Robinson (1983–1984) Irving Kaplansky (1985–1986) George Mostow (1987–1988) William Browder (1989–1990) Michael
William_Fogg_Osgood
German-American mathematician
(1979–1980) Andrew M. Gleason (1981–1982) Julia Robinson (1983–1984) Irving Kaplansky (1985–1986) George Mostow (1987–1988) William Browder (1989–1990) Michael
Richard_Brauer
American mathematician (1876–1943)
(1979–1980) Andrew M. Gleason (1981–1982) Julia Robinson (1983–1984) Irving Kaplansky (1985–1986) George Mostow (1987–1988) William Browder (1989–1990) Michael
Earle_Raymond_Hedrick
Teaching award by the University of Chicago
Cawelti 1963: Richard Lashof, McKim Marriott 1962: Edward Wasiolek 1961: Irving Kaplansky 1960: Karl Weintraub 1959: Lawrence Bogorad 1958: Stuart Tave, Maynard
Quantrell_Award
American mathematician (1858–1928)
(1979–1980) Andrew M. Gleason (1981–1982) Julia Robinson (1983–1984) Irving Kaplansky (1985–1986) George Mostow (1987–1988) William Browder (1989–1990) Michael
Henry_Burchard_Fine
English–American mathematician (1860–1937)
(1979–1980) Andrew M. Gleason (1981–1982) Julia Robinson (1983–1984) Irving Kaplansky (1985–1986) George Mostow (1987–1988) William Browder (1989–1990) Michael
Frank_Morley
American mathematician
(1979–1980) Andrew M. Gleason (1981–1982) Julia Robinson (1983–1984) Irving Kaplansky (1985–1986) George Mostow (1987–1988) William Browder (1989–1990) Michael
Ruth_Charney
American mathematician (1892–1977)
(1979–1980) Andrew M. Gleason (1981–1982) Julia Robinson (1983–1984) Irving Kaplansky (1985–1986) George Mostow (1987–1988) William Browder (1989–1990) Michael
Marston_Morse
American mathematician (born 1947)
(1979–1980) Andrew M. Gleason (1981–1982) Julia Robinson (1983–1984) Irving Kaplansky (1985–1986) George Mostow (1987–1988) William Browder (1989–1990) Michael
David_Eisenbud
Canadian mathematician (born 1944)
(1979–1980) Andrew M. Gleason (1981–1982) Julia Robinson (1983–1984) Irving Kaplansky (1985–1986) George Mostow (1987–1988) William Browder (1989–1990) Michael
James_Arthur_(mathematician)
American mathematician (1927–2016)
(1979–1980) Andrew M. Gleason (1981–1982) Julia Robinson (1983–1984) Irving Kaplansky (1985–1986) George Mostow (1987–1988) William Browder (1989–1990) Michael
Felix_Browder
American mathematician (1923–2017)
(1979–1980) Andrew M. Gleason (1981–1982) Julia Robinson (1983–1984) Irving Kaplansky (1985–1986) George Mostow (1987–1988) William Browder (1989–1990) Michael
George_Mostow
Set of finitely supported functions from a group to a ring
of complex numbers is probably the one best studied. In this case, Irving Kaplansky proved that if a and b are elements of C[G] with ab = 1, then ba =
Group_ring
Branch of mathematics
other mathematical objects being called Noetherian. Noted algebraist Irving Kaplansky called this work "revolutionary"; results which seemed inextricably
Abstract_algebra
In mathematics, dimension of a ring
Noetherian Rings (2001). Amer. Math. Soc., Providence. Corollary 6.4.8. Irving Kaplansky, Commutative rings (revised ed.), University of Chicago Press, 1974
Krull_dimension
American mathematician (1934–2025)
(1979–1980) Andrew M. Gleason (1981–1982) Julia Robinson (1983–1984) Irving Kaplansky (1985–1986) George Mostow (1987–1988) William Browder (1989–1990) Michael
William Browder (mathematician)
William_Browder_(mathematician)
Problem in Lie group theory
group, Osaka Mathematical Journal v.2, no. 1 Mar. (1950), 13–14. Irving Kaplansky, Lie Algebras and Locally Compact Groups, Chicago Lectures in Mathematics
Hilbert's_fifth_problem
American mathematician
(1979–1980) Andrew M. Gleason (1981–1982) Julia Robinson (1983–1984) Irving Kaplansky (1985–1986) George Mostow (1987–1988) William Browder (1989–1990) Michael
Ken_Ribet
Russian-American mathematician (1899–1986)
(1979–1980) Andrew M. Gleason (1981–1982) Julia Robinson (1983–1984) Irving Kaplansky (1985–1986) George Mostow (1987–1988) William Browder (1989–1990) Michael
Oscar_Zariski
Association of professional mathematicians
Peter Lax (1979–80) Andrew Gleason (1981–82) Julia Robinson (1983–84) Irving Kaplansky (1985–86) George Mostow (1987–88) William Browder (1989–90) Michael
American_Mathematical_Society
Branch of algebra
conditions with regard to (mathematical) ideals. Noted algebraist Irving Kaplansky called this work "revolutionary"; the publication gave rise to the
Ring_theory
American mathematician (born 1937)
(1979–1980) Andrew M. Gleason (1981–1982) Julia Robinson (1983–1984) Irving Kaplansky (1985–1986) George Mostow (1987–1988) William Browder (1989–1990) Michael
Arthur_Jaffe
Jarník Mark Kac Paul Chester Kainen Shizuo Kakutani Egbert van Kampen Irving Kaplansky Jovan Karamata Ke Zhao Paul Kelly Péter Kiss Murray S. Klamkin Maria
List of people by Erdős number
List_of_people_by_Erdős_number
Canadian mathematician (1923–2017)
(1979–1980) Andrew M. Gleason (1981–1982) Julia Robinson (1983–1984) Irving Kaplansky (1985–1986) George Mostow (1987–1988) William Browder (1989–1990) Michael
Cathleen_Synge_Morawetz
American mathematician
teaching, and for his solution to a long-standing open problem due to Irving Kaplansky on a symmetric *-algebra. Robert Stuart Doran was born on December
Robert_S._Doran
American mathematician
(1979–1980) Andrew M. Gleason (1981–1982) Julia Robinson (1983–1984) Irving Kaplansky (1985–1986) George Mostow (1987–1988) William Browder (1989–1990) Michael
Edward_J._McShane
American mathematician
(1979–1980) Andrew M. Gleason (1981–1982) Julia Robinson (1983–1984) Irving Kaplansky (1985–1986) George Mostow (1987–1988) William Browder (1989–1990) Michael
Raymond_Louis_Wilder
Commutative group (mathematics)
abelian groups has been one avenue of further progress. See the books by Irving Kaplansky, László Fuchs, Phillip Griffith, and David Arnold, as well as the proceedings
Abelian_group
American mathematician
(1979–1980) Andrew M. Gleason (1981–1982) Julia Robinson (1983–1984) Irving Kaplansky (1985–1986) George Mostow (1987–1988) William Browder (1989–1990) Michael
Gilbert_Ames_Bliss
Research institute
Image Name Timespan Shiing-Shen Chern 1982–1984 Irving Kaplansky 1984–1992 William Thurston 1992–1997 David Eisenbud 1997–2007 Robert Bryant 2007–2013
Simons Laufer Mathematical Sciences Institute
Simons_Laufer_Mathematical_Sciences_Institute
American mathematician (1910–1999)
(1979–1980) Andrew M. Gleason (1981–1982) Julia Robinson (1983–1984) Irving Kaplansky (1985–1986) George Mostow (1987–1988) William Browder (1989–1990) Michael
Nathan_Jacobson
American mathematician
(1979–1980) Andrew M. Gleason (1981–1982) Julia Robinson (1983–1984) Irving Kaplansky (1985–1986) George Mostow (1987–1988) William Browder (1989–1990) Michael
Henry_Seely_White
Abstract ring with finite number of elements
MR 0022841, Zbl 0031.10802 Scorza 1935, see review of Ballieu by Irving Kaplansky in Mathematical Reviews Antipkin, V. G.; Elizarov, V. P. (1982), "Rings
Finite_ring
Concept in projective geometry
Correlations and semi-bilinear forms, Dover Publications ISBN 0-486-43835-X Irving Kaplansky (1974) [1969], Linear Algebra and Geometry (2nd ed.), p. 104 Robert
Correlation (projective geometry)
Correlation_(projective_geometry)
Algebra of formal sums
choice) can be found in Serge Lang's Algebra. Solomon Lefschetz and Irving Kaplansky argue that using the well-ordering principle in place of Zorn's lemma
Free_abelian_group
American mathematician (1876–1965)
(1979–1980) Andrew M. Gleason (1981–1982) Julia Robinson (1983–1984) Irving Kaplansky (1985–1986) George Mostow (1987–1988) William Browder (1989–1990) Michael
Luther_P._Eisenhart
Public research university in Ontario, Canada
Best, geologists Joseph Tyrrell and John Tuzo Wilson, mathematicians Irving Kaplansky and William Kahan, physicists Arthur Leonard Schawlow and Bertram Brockhouse
University_of_Toronto
American mathematician
(1979–1980) Andrew M. Gleason (1981–1982) Julia Robinson (1983–1984) Irving Kaplansky (1985–1986) George Mostow (1987–1988) William Browder (1989–1990) Michael
James_Glimm
Zero divisors in a module
algebra and algebraic geometry", Birkhauser 1985, ISBN 0-8176-3065-1 Irving Kaplansky, "Infinite abelian groups", University of Michigan, 1954. Michiel Hazewinkel
Torsion_(algebra)
Annual mathematics competition
Name (School) Year (s) George W. Mackey (Rice) 1938 Irving Kaplansky (Toronto) 1938 Michael J. Norris (College of St. Thomas) 1938 Robert W. Gibson (Fort
Putnam_Competition
American mathematician (born 1954)
(1979–1980) Andrew M. Gleason (1981–1982) Julia Robinson (1983–1984) Irving Kaplansky (1985–1986) George Mostow (1987–1988) William Browder (1989–1990) Michael
David_Vogan
American mathematician (1878–1966)
(1979–1980) Andrew M. Gleason (1981–1982) Julia Robinson (1983–1984) Irving Kaplansky (1985–1986) George Mostow (1987–1988) William Browder (1989–1990) Michael
Arthur_Byron_Coble
Hungarian-born American mathematician (1926–2025)
(1979–1980) Andrew M. Gleason (1981–1982) Julia Robinson (1983–1984) Irving Kaplansky (1985–1986) George Mostow (1987–1988) William Browder (1989–1990) Michael
Peter_Lax
Invariant in projective geometry
presentation by Cornell University Historical Mathematical Monographs. Irving Kaplansky (1969). Linear Algebra and Geometry: A Second Course. Courier Corporation
Cross-ratio
American mathematician (1869-1950)
(1979–1980) Andrew M. Gleason (1981–1982) Julia Robinson (1983–1984) Irving Kaplansky (1985–1986) George Mostow (1987–1988) William Browder (1989–1990) Michael
Virgil_Snyder
American mathematician (1880–1960)
(1979–1980) Andrew M. Gleason (1981–1982) Julia Robinson (1983–1984) Irving Kaplansky (1985–1986) George Mostow (1987–1988) William Browder (1989–1990) Michael
Oswald_Veblen
American mathematician (1867–1918)
(1979–1980) Andrew M. Gleason (1981–1982) Julia Robinson (1983–1984) Irving Kaplansky (1985–1986) George Mostow (1987–1988) William Browder (1989–1990) Michael
Maxime_Bôcher
1972 Philip J. Davis 1971 W. T. Tutte 1970 W. A. J. Luxemburg 1969 R. Pyke 1968 Irving Kaplansky List of mathematics awards Canadian Mathematical Society
Jeffery–Williams_Prize
American mathematician
(1979–1980) Andrew M. Gleason (1981–1982) Julia Robinson (1983–1984) Irving Kaplansky (1985–1986) George Mostow (1987–1988) William Browder (1989–1990) Michael
John_Howard_Van_Amringe
American mathematician
(1979–1980) Andrew M. Gleason (1981–1982) Julia Robinson (1983–1984) Irving Kaplansky (1985–1986) George Mostow (1987–1988) William Browder (1989–1990) Michael
Robert_Lee_Moore
American mathematician (1884–1944)
(1979–1980) Andrew M. Gleason (1981–1982) Julia Robinson (1983–1984) Irving Kaplansky (1985–1986) George Mostow (1987–1988) William Browder (1989–1990) Michael
George_David_Birkhoff
American mathematical astronomer (1838–1914)
(1979–1980) Andrew M. Gleason (1981–1982) Julia Robinson (1983–1984) Irving Kaplansky (1985–1986) George Mostow (1987–1988) William Browder (1989–1990) Michael
George_William_Hill
American mathematician (1862–1932)
(1979–1980) Andrew M. Gleason (1981–1982) Julia Robinson (1983–1984) Irving Kaplansky (1985–1986) George Mostow (1987–1988) William Browder (1989–1990) Michael
E._H._Moore
German-American mathematician (1926–2007)
University of Chicago, with a doctoral thesis on ring theory supervised by Irving Kaplansky. After postdoctoral studies at the University of Michigan, Rosenberg
Alex_F._T._W._Rosenberg
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