Irving Kaplansky
Irving Kaplansky (Toronto, 22 de março de 1917 — Los Angeles, 25 de junho de 2006) foi um matemático canadense.
Contribuições matemáticas
Kaplansky fez grandes contribuições para a teoria dos grupos, teoria dos anéis, teoria das álgebras de operadores e teoria de campos e criou o teorema da densidade de Kaplansky, o jogo de Kaplansky e a conjectura de Kaplansky. Ele publicou mais de 150 artigos e 11 livros matemáticos.
Kaplansky foi o supervisor de doutorado de 55 alunos, incluindo os notáveis matemáticos Hyman Bass, Susanna S. Epp, Günter Lumer, Eben Matlis, Donald Ornstein, Ed Posner, Alex F. T. W. Rosenberg, Judith D. Sally e Harold Widom.
Publicações selecionadas
Livros
com I. N. Herstein: —— (1974). Matters mathematical. : New York, Harper & Row. ISBN 9780060428037 2nd edn. 1978
Artigos
- Kaplansky, Irving (1944). «Symbolic solution of certain problems in permutations». Bull. Amer. Math. Soc. 50 (12): 906–914. MR 0011393. doi:10.1090/s0002-9904-1944-08261-x
- Kaplansky, Irving (1945). «A note on groups without isomorphic subgroups». Bull. Amer. Math. Soc. 51 (8): 529–530. MR 0012267. doi:10.1090/s0002-9904-1945-08382-7
- with I. S. Cohen: Cohen, I. S.; Kaplansky, Irving (1946). «Rings with a finite number of primes. I». Trans. Amer. Math. Soc. 60: 468–477. MR 0019595. doi:10.1090/s0002-9947-1946-0019595-7
- Kaplansky, Irving (1946). «On a problem of Kurosch and Jacobson». Bull. Amer. Math. Soc. 52 (6): 496–500. MR 0016758. doi:10.1090/s0002-9904-1946-08600-0
- Kaplansky, Irving (1947). «Lattices of continuous functions». Bull. Amer. Math. Soc. 53 (6): 617–623. MR 0020715. doi:10.1090/s0002-9904-1947-08856-x
- com Richard F. Arens: Arens, Richard F.; Kaplansky, Irving (1948). «Topological representations of algebras». Trans. Amer. Math. Soc. 63 (3): 457–481. MR 0025453. doi:10.1090/s0002-9947-1948-0025453-6
- Kaplansky, Irving (1948). «Rings with a polynomial identity». Bull. Amer. Math. Soc. 54 (6): 575–580. MR 0025451. doi:10.1090/s0002-9904-1948-09049-8
- «Topological rings». Bull. Amer. Math. Soc. 54: 909–916. 1948. MR 0027269. doi:10.1090/S0002-9904-1948-09096-6
- Kaplansky, Irving (1949). «Elementary divisors and modules». Trans. Amer. Math. Soc. 66 (2): 464–491. MR 0031470. doi:10.1090/s0002-9947-1949-0031470-3
- Kaplansky, I. (1949). «Primary ideals in group algebras». Proc Natl Acad Sci U S A. 35 (3): 133–136. Bibcode:1949PNAS...35..133K. PMC 1062983. PMID 16588871. doi:10.1073/pnas.35.3.133
- Kaplansky, Irving (1950). «Topological representations of algebras. II». Trans. Amer. Math. Soc. 68: 62–75. MR 0032612. doi:10.1090/s0002-9947-1950-0032612-4
- Kaplansky, Irving (1950). «The Weierstrass theorem in fields with valuations». Proc. Amer. Math. Soc. 1 (3): 356–357. MR 0035760. doi:10.1090/s0002-9939-1950-0035760-3
- Kaplansky, Irving (1951). «The structure of certain operator algebras». Trans. Amer. Math. Soc. 70 (2): 219–255. MR 0042066. doi:10.1090/s0002-9947-1951-0042066-0
- Kaplansky, Irving (1952). «Modules over Dedekind rings and valuations rings». Trans. Amer. Math. Soc. 72 (2): 327–340. MR 0046349. doi:10.1090/s0002-9947-1952-0046349-0
- Kaplansky, Irving (1952). «Orthogonal similarity in infinite dimensional spaces». Proc. Amer. Math. Soc. 3: 16–25. MR 0046564. doi:10.1090/s0002-9939-1952-0046564-1
- Kaplansky, Irving (1952). «Symmetry of Banach algebras». Proc. Amer. Math. Soc. 3 (3): 396–399. MR 0048711. doi:10.1090/s0002-9939-1952-0048711-4
- Kaplansky, I. (1952). «Some results on abelian groups». Proc Natl Acad Sci U S A. 38 (6): 538–540. Bibcode:1952PNAS...38..538K. PMC 1063607. PMID 16589142. doi:10.1073/pnas.38.6.538
- Kaplansky, Irving (1953). «Infinite dimensional quadratic forms admitting composition». Proc. Amer. Math. Soc. 4 (6): 956–960. MR 0059895. doi:10.1090/s0002-9939-1953-0059895-7
- Kaplansky, Irving (1953). «Dual modules over a valuation ring. I». Proc. Amer. Math. Soc. 4 (2): 213–219. MR 0053092. doi:10.1090/s0002-9939-1953-0053092-7
- Kaplansky, Irving (1958). «Lie algebras of characteristic p». Trans. Amer. Math. Soc. 89: 149–183. MR 0099359. doi:10.1090/s0002-9947-1958-0099359-7
- Kaplansky, Irving (1962). «Decomposability of modules». Proc. Amer. Math. Soc. 13 (4): 532–535. MR 0137738. doi:10.1090/s0002-9939-1962-0137738-6
- Kaplansky, Irving (1980). «Superalgebras». Pacific J. Math. 86 (1): 93–98. doi:10.2140/pjm.1980.86.93
- Kaplansky, Irving (1994). «A quasi-commutative ring that is not neo-commutative». Proc. Amer. Math. Soc. 122: 321. MR 1257114. doi:10.1090/s0002-9939-1994-1257114-3
- «The forms x+32y2 and x+64y2 ». Proc. Amer. Math. Soc. 131: 2299–2300. 2003. MR 1963780. doi:10.1090/s0002-9939-03-07022-9
Referências
- ↑ Irving Kaplansky (em inglês) no Mathematics Genealogy Project
- ↑ «Irving Kaplansky - Biography». Maths History (em inglês). Consultado em 22 de março de 2023
- ↑ «Irving Kaplansky - The Mathematics Genealogy Project». mathgenealogy.org. Consultado em 22 de março de 2023
- ↑ Baer, Reinhold (1955). «Review: Infinite abelian groups by I. Kaplansky» (PDF). Bull. Amer. Math. Soc. 61 (1): 88–89. doi:10.1090/s0002-9904-1955-09877-x
Bibliografia
Ligações externas
Prêmio Leroy P. Steele (1970 — 2019) |
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Agraciados até 1978 |
1970: Solomon Lefschetz •
1971: James Baldwin Carrell, Jean Dieudonné e Phillip Griffiths •
1972: Edward Baldwin Curtis, William John Ellison, Lawrence Edward Payne e Dana Scott •
1975: Lipman Bers, Martin Davis, Herbert Blaine Lawson, George Mackey e Joseph Lawrence Taylor
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Contribuição Fundamental à Investigação Científica |
1979: Joseph Kohn e Hans Lewy •
1980: Gerhard Hochschild •
1981: Eberhard Hopf •
1982: John Milnor •
1983: Stephen Kleene •
1984: Lennart Carleson •
1985: Robert Steinberg •
1986: Rudolf Kalman •
1987: Herbert Federer e Wendell Fleming •
1988: Gian-Carlo Rota •
1989: Alberto Calderón •
1990: Bertram Kostant •
1991: Eugenio Calabi •
1992: James Glimm •
1993: George Mostow •
1994: Louis de Branges de Bourcia •
1995: Edward Nelson •
1996: Daniel Stroock e S. R. Srinivasa Varadhan •
1997: Mikhael Gromov •
1998: Herbert Wilf e Doron Zeilberger •
1999: Michael Crandall e John Forbes Nash •
2000: Barry Mazur •
2001: Leslie Greengard e Vladimir Rokhlin •
2002: Mark Goresky e Robert MacPherson •
2003: Ronald Jensen e Michael Morley •
2004: Lawrence Craig Evans e Nicolai Krylov •
2005: Robert Langlands •
2006: Clifford Gardner, John Greene, Martin Kruskal e Robert Miura •
2007: Karen Uhlenbeck •
2008: Endre Szemerédi •
2009: Richard Hamilton •
2010: Robert Griess •
2011: Ingrid Daubechies •
2012: William Thurston •
2013: Saharon Shelah •
2014: Luis Caffarelli, Robert Kohn e Louis Nirenberg •
2015: Rostislav Grigorchuk •
2016: Andrew Majda •
2017: Leon Simon •
2018: Sergey Fomin e Andrei Zelevinsky
2019: Haruzo Hida
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Carreira |
1979: Salomon Bochner e Antoni Zygmund •
1980: André Weil •
1981: Oscar Zariski •
1982: Fritz John •
1983: Shiing-Shen Chern •
1984: Joseph Leo Doob •
1985: Hassler Whitney •
1986: Saunders Mac Lane •
1987: Samuel Eilenberg •
1988: Deane Montgomery •
1989: Irving Kaplansky •
1990: Raoul Bott •
1991: Armand Borel •
1992: Peter Lax •
1993: Eugene Dynkin •
1994: Louis Nirenberg •
1995: John Tate •
1996: Goro Shimura •
1997: Ralph Phillips •
1998: Nathan Jacobson •
1999: Richard Kadison •
2000: Isadore Singer •
2001: Harry Kesten •
2002: Michael Artin e Elias Stein •
2003: Ronald Graham e Victor Guillemin •
2004: Cathleen Synge Morawetz •
2005: Israel Gelfand •
2006: Frederick Gehring e Dennis Sullivan •
2007: Henry McKean •
2008: George Lusztig •
2009: Luis Caffarelli •
2010: William Fulton •
2011: John Milnor •
2012: Ivo Babuška •
2013: Yakov G. Sinai •
2014: Phillip Griffiths •
2015: Victor Kac •
2016: Barry Simon •
2017: James Arthur •
2018: Jean Bourgain •
2019: Jeff Cheeger
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Divulgação da Matemática |
1979: Robin Hartshorne •
1980: Harold Edwards •
1981: Nelson Dunford e Jacob Theodore Schwartz •
1982: Tsit Yuen Lam •
1983: Paul Halmos •
1984: Elias Stein •
1985: Michael Spivak •
1986: Donald Knuth •
1987: Martin Gardner •
1988: Sigurdur Helgason •
1989: Daniel Gorenstein •
1990: Robert Richtmyer •
1991: François Treves •
1992: Jacques Dixmier •
1993: Walter Rudin •
1994: Ingrid Daubechies •
1995: Jean-Pierre Serre •
1996: Bruce Berndt e William Fulton •
1997: Anthony Knapp •
1998: Joseph Hillel Silverman •
1999: Serge Lang •
2000: John Conway •
2001: Richard Peter Stanley •
2002: Yitzhak Katznelson •
2003: John Garnett •
2004: John Milnor •
2005: Branko Grünbaum •
2006: Lars Hörmander •
2007: David Mumford •
2008: Neil Trudinger •
2009: Ian Macdonald •
2010: David Eisenbud •
2011: Henryk Iwaniec •
2012: Michael Aschbacher, Richard Lyons, Steven Smith e Ronald Solomon •
2013: John Guckenheimer e Philip Holmes •
2014: Dmitri Burago, Yuri Burago e Sergei Ivanov •
2015: Robert Lazarsfeld •
2016: David Archibald Cox, John Little e Donal O’Shea •
2017: Dusa McDuff e Dietmar Arno Salamon •
2018: Martin Aigner e Günter Matthias Ziegler
2019: Philippe Flajolet e Robert Sedgewick
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