Irving Kaplansky

Q: What Schools Are Affiliated With Irving Kaplansky

Irving Kaplansky is affiliated with the following schools: University of Chicago, University of Toronto, Harvard University

Irving Kaplansky's AcademicInfluence.com Rankings

Irving Kaplansky

Mathematics

#120

World Rank

#303

Historical Rank

Measure Theory

#177

World Rank

#273

Historical Rank

mathematics Degrees

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Mathematics

Why Is Irving Kaplansky Influential?

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According to Wikipedia, Irving Kaplansky was a mathematician, college professor, author, and amateur musician. Biography Kaplansky or "Kap" as his friends and colleagues called him was born in Toronto, Ontario, Canada, to Polish-Jewish immigrants; his father worked as a tailor, and his mother ran a grocery and, eventually, a chain of bakeries. He went to Harbord Collegiate Institute receiving the Prince of Wales Scholarship as a teenager. He attended the University of Toronto as an undergraduate and finished first in his class for three consecutive years. In his senior year, he competed in the first William Lowell Putnam Mathematical Competition, becoming one of the first five recipients of the Putnam Fellowship, which paid for graduate studies at Harvard University. Administered by the Mathematical Association of America, 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 despite being attempted by students specializing in mathematics."

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Irving Kaplansky's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

An introduction to differential algebra (1957) (647)
Infinite Abelian groups (1954) (554)
Elementary divisors and modules (1949) (407)
Fields and rings (1969) (373)
Modules over Dedekind rings and valuation rings (1952) (302)
Rings of operators (1956) (286)
PROJECTIONS IN BANACH ALGEBRAS (1951) (267)
Maximal fields with valuations, II (1942) (254)
The structure of certain operator algebras (1951) (225)
Modules Over Operator Algebras (1953) (208)
Topological representation of algebras (1948) (201)
Rings with a polynomial identity (1948) (181)
Algebras of Type I (1952) (140)
Algebraic and analytic aspects of operator algebras (1970) (127)
Any Orthocomplemented Complete Modular Lattice is a Continuous Geometry (1955) (107)
Lie Algebras And Locally Compact Groups (1971) (103)
A Contribution to Von Neumann's Theory of Games (1945) (102)
Lattices of continuous functions (1947) (102)
The problem of the rooks and its applications (1946) (99)
Groups with Representations of Bounded Degree (1949) (97)
Topological representation of algebras. II (1950) (92)
Harish-Chandra Modules Over the Virasoro Algebra (1985) (87)
A theorem on rings of operators (1951) (83)
Solution of the “Problème des ménages” (1943) (80)
Rings for which every module is a direct sum of cyclic modules (1951) (79)
Infinite-dimensional quadratic forms admitting composition (1953) (79)
"Problems in the Theory of Rings" Revisited (1970) (78)
There are 913 regular ternary forms (1997) (72)
A Common Error concerning Kurtosis (1945) (64)
Linear Algebra and Geometry: A Second Course (2003) (61)
Linear algebra and geometry (1969) (59)
Semi-automorphisms of rings (1947) (59)
Ring Isomorphisms of Banach Algebras (1954) (53)
Symbolic solution of certain problems in permutations (1944) (51)
A Theorem on Division Rings (1951) (51)
The Weierstrass theorem in fields with valuations (1950) (48)
Topological methods in valuation theory (1947) (47)
The Asymptotic Number of Latin Rectangles (1946) (45)
The Asymptotic Distribution of Runs of Consecutive Elements (1945) (43)
Set theory and metric spaces (1972) (42)
The Virasoro algebra (1982) (40)
Lie algebras of characteristic (1958) (39)
Dual modules over a valuation ring. I (1953) (36)
“Problems in the Theory of Rings” Revisited (1970) (35)
The splitting of modules over integral domains (1962) (33)
Submodules of Quaternion Algebras (1969) (31)
Locally Compact Rings (1948) (31)
The Homological Dimension of a Quotient Field (1966) (30)
Topics in commutative ring theory (1974) (28)
Primary Ideals in Group Algebras. (1949) (27)
Lattices of Continuous Functions II (1948) (27)
Rings with a finite number of primes. I (1946) (25)
Some Results on Abelian Groups. (1952) (25)
Ternary positive quadratic forms that represent all odd positive integers (1995) (25)
Group algebras in the large (1951) (25)
Some aspects of analysis and probability (1960) (25)
Fröhlich's local quadratic forms. (1969) (24)
On the Dimension of Modules and Algebras, X: A Right Hereditary Ring which is not left Hereditary (1958) (24)
Coxeter Graphs and Towers of Algebras (2011) (23)
Hilbert's problems (1977) (22)
Some simple Lie algebras of characteristic 2 (1982) (22)
Homological dimension of rings and modules (1958) (22)
The Engel–Kolchin theorem revisited (1977) (21)
Algebraic polar decomposition (1990) (20)
Selected papers and other writings (1995) (19)
The first nontrivial genus of positive definite ternary forms (1995) (19)
Composition of binary quadratic forms (1968) (18)
R-Sequences and Homological Dimension (1962) (17)
Algebras with Many Derivations (1986) (16)
On a problem of Kurosch and Jacobson (1946) (16)
Polynomials in topological fields (1948) (15)
LOCALLY COMPACT RINGS. III. (1951) (15)
Three-dimensional division algebras (1976) (15)
Infinite-dimensional lie algebras. II (1975) (14)
THE COLLECTED PAPERS OF EMIL ARTIN (1967) (13)
Products of normal operators (1953) (13)
Adjacent prime ideals (1972) (12)
A Generalization of Ulm’s Theorem (1995) (12)
On a Generalization of the "Probleme des Rencontres" (1939) (12)
Sums of Squares, Cubes, and Higher Powers (1995) (12)
A contribution to von Neumann's theory of games. II (1995) (12)
Review: Felix E. Browder, Mathematical developments arising from Hilbert problems (1977) (10)
Multiple Matching and Runs by the Symbolic Method (1945) (9)
Equal sums of sixth powers (1974) (9)
Some remarks on relatively complete fields (1942) (8)
Completely continuous normal operators with property $L$. (1953) (8)
Representations of separable algebras (1952) (8)
Notes on ring theory (1965) (7)
Symmetry of Banach algebras (1952) (7)
Abstract Quadratic Forms (1969) (7)
Nilpotent elements in Lie algebras (1990) (6)
A note on groups without isomorphic subgroups (1945) (5)
The Early Work of Saunders Mac Lane on Valuations and Fields (1979) (4)
Determinants of matrices of the conference type (1997) (4)
$Z_{2}$-graded algebras (1991) (4)
A quasi-commutative ring that is not neo-commutative (1994) (4)
Orthogonal similarity in infinite-dimensional spaces (1952) (4)
The forms +32² and +64² (2003) (4)
DECOMPOSABILITY OF MODULES (1962) (4)
Saunders Mac Lane Selected Papers (1979) (4)
The forms x + 32y2 and x + 64y2 (2003) (4)
A second genus of regular ternary forms (1995) (3)
Jacobson's Lemma revisited (1980) (3)
Lucas's Tests for Mersenne Numbers (1945) (3)
The first summer mathematical institute (1954) (3)
Five theorems on abelian groups (1978) (2)
A cofinal coloring theorem for partially ordered algebras (1985) (2)
Integers Uniquely Represented by Certain Ternary Forms (2013) (2)
MSRI after three years (1985) (1)
Problems for Solution: 4341-4345 (1949) (1)
Mathematics vs. Numerical Analysis. (1965) (1)
A Characterization of the Normal Distribution (1943) (1)
The Theory of Homological Dimension (2010) (1)
A survey of operator algebras . The opening of Jeffery Hall . The responsibility of the scientist today (1971) (1)
Review: R. Baer, Linear algebra and projective geometry (1953) (1)
Problems for Solution: E401-E405 (1940) (1)
C{CR}-rings. (1989) (0)
Now it happens that in the three-dimensional case the twisted fields introduced (1975) (0)
A Common Error concerning Kurtosis (1945) (0)
A survey of operator algebras (1971) (0)
Problems for Solution: E681-E685 (1945) (0)
( 1910 – 1999 ) (2000) (0)
Problems and Solutions: 4234-4238 (1947) (0)
Parallel and distributed computing. Final report, 15 August 1985-14 August 1986 (1986) (0)
Parallel and distributed computing. Final report, 1 June 1985-30 November 1986 (1986) (0)
The theory of fields (1965) (0)
Parallel and Distributed Computing. (1986) (0)
A New Stability Test for Two-Dimensional Discrete Systems Using Bilinear Continuous Fractions (1989) (0)
Problems for Solution: 4295-4299 (1948) (0)
Emmy Noether, 1882–1935. By Auguste Dick (1983) (0)
Exploratory Research in Mathematics. (1971) (0)
Indefinite binary quadratic forms with Markov ratio exceeding 9 (2003) (0)
SYMMETRY OF BANACH ALGEBRAS1 (2010) (0)
Problems for Solution: E661-E665,E637 (1945) (0)
Review: Helmut Hasse, Number theory (1981) (0)
Some Aspects of Analysis and Probability. Vol. 4, Surveys in Applied Mathematics. (1960) (0)
Emmy Noether, 1882-1935.@@@Emmy Noether, A Tribute to Her Life and Work. (1983) (0)
Advanced Problems: 5689-5694 (1969) (0)
INVESTIGATIONS IN ALGEBRAS AND FINITE FIELDS (1961) (0)
Mathematics vs. Numerical Analysis (1965) (0)
A curious property of three-by-three matrices and an application to orders (1973) (0)
ORTHOGONAL SIMILARITY IN INFINITE- DIMENSIONAL SPACES1 (2010) (0)
Finite groups : proceedings of a Symposium in Pure Mathematics of the American Mathematical Society, held in New York, April 23-24, 1959, cosponsored by The Institute for Defense Analysis (1959) (0)
Advanced Problems: 5658-5664 (1969) (0)
Title A generalization of a theorem of I (0)
Problems for Solution: 4171-4175 (1945) (0)
Note on the preceding paper (1945) (0)
Introduction to the Theory of Finite Groups.Walter Ledermann. Interscience, New York, andOliver and Boyd, Edinburgh-London, rev. ed., 1953.160 pp. $1.55 (1954) (0)
Book Review: Topological rings (1994) (0)
Problems for Solution: E759,E766-E770 (1947) (0)

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What Schools Are Affiliated With Irving Kaplansky?

Irving Kaplansky is affiliated with the following schools:

Irving Kaplansky's Academic­Influence.com Rankings