Irving Kaplansky

Irving Kaplansky ( born March 22, 1917 in Toronto, Ontario, † June 25, 2006 in Los Angeles ) was an American mathematician who worked on algebra.

Life and work

Kaplansky was the son of Polish parents who immigrated to Canada shortly before his birth. He studied at the University of Toronto, where in 1938 his bachelor's and his master's degree in 1940 and made ​​at the same time was the winner of the Putnam Competition. As winner of the competition, he was able to continue ( the first Putnam Fellow ) graduated from Harvard University, where he received his doctorate in 1941 by Saunders MacLane ( as his first PhD student ) (Maximal Fields with Valuations ). In 1940 he took the U.S. citizenship. As a post-doc, he was at Harvard until 1944 Benjamin Peirce Instructor. In 1945 he went - after war-related activities at Columbia University - to the University of Chicago, where he became a professor and remained until his retirement in 1984. 1962 to 1967 he was Chairman and faculty there in 1969, " George Herbert Mead Distinguished Service Professor ". After his retirement, he was director of the Mathematical Sciences Research Institute in Berkeley.

Kaplansky dealt with the various areas of algebra with commutative algebra, ring theory, field theory, group theory, Banach algebras. He is also known for his textbooks. The leak rate of Kaplansky is associated with his name. He led a algebras with polynomial identity.

In 1975, he was vice president of the American Mathematical Society (AMS) and 1985/86 President. 1947 to 1952 he was associate editor of the Bulletin of the AMS. He was Guggenheim Fellow and a member of the National Academy of Sciences and the American Academy of Arts and Sciences. In 1987 he was made an honorary member of the London Mathematical Society. In 1989 he received the Leroy P. Steele Prize of the AMS.

He is the father of singer Lucy Kaplansky ( born 1960 ), who is also a psychiatrist. Kaplansky was an accomplished pianist and took in Chicago performances of operas of Gilbert and Sullivan in part. He also composed songs with mathematical overtones such as A Song of Pi ( the melody is based on the first digits of ).

His doctoral include Donald Samuel Ornstein, Joseph Rotman, Harold Widom, Hyman Bass, Günter Lumer.

Writings

  • Commutative ring. University of Chicago Press, 1970.
  • Infinite Abelian Groups.
  • Fields and rings. 2nd edition 1972.
  • An introduction to differential algebra. In 1957.
  • Lie algebras and locally compact groups. In 1971.
  • Projective modules, Ann. of Math ( 2) 1958 68 372-377. ( Every projective module is the direct sum of countably generated projective modules. )
  • Modules over operator algebras, Amer. J. Math 75 ( 1953). 839-858.
  • Projections in Banach algebras, Ann. of Math ( 2) 53, ( 1951). 235-249.
  • Maximum fields with valuations, Duke Math J. 9 (1942 ). 303-321.
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