Irving Kaplansky

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Irving Kaplansky, 1984

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

Live and act

Kaplansky was the son of Polish parents who immigrated to Canada shortly before he was born. He studied at the University of Toronto , where he made his bachelor's degree in 1938 and his master's degree in 1940 and was also the winner of the Putnam competition. As the winner of the competition, he (as the first Putnam Fellow) was able to continue his studies at Harvard University , where he received his doctorate in 1941 with Saunders MacLane (as his first doctoral student) ( Maximal Fields with Valuations ). In 1940 he became a US citizen. As a post-doc he was a Benjamin Peirce instructor at Harvard until 1944. In 1945 he went - after working at Columbia University due to the war - to the University of Chicago , where he became a professor and stayed until his retirement in 1984. From 1962 to 1967 he was chairman of the faculty there and in 1969 became "George Herbert Mead Distinguished Service Professor". After his retirement he became director of the Mathematical Sciences Research Institute in Berkeley .

Kaplansky dealt with the most diverse areas of algebra: with commutative algebra, ring theory, body theory, group theory, Banach algebra. He is also known for his textbooks. The leak rate of Kaplansky is connected with his name. He introduced algebras with polynomial identity.

Kaplansky was elected to the American Academy of Arts and Sciences in 1965, and to the National Academy of Sciences in 1966 . In 1975 he was Vice President of the American Mathematical Society (AMS) and President 1985/86. From 1947 to 1952 he was co-editor of the Bulletin of the AMS. He was a Guggenheim Fellow and in 1987 he became an honorary member of the London Mathematical Society . In 1989 he received the AMS Leroy P. Steele Prize .

He is the father of the singer Lucy Kaplansky (* 1960), who is also a psychiatrist. Kaplansky was an accomplished pianist and has performed in Chicago in operas by Gilbert and Sullivan. He also composed songs with mathematical echoes like A Song of Pi (the melody is based on the first decimal places of ).

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


  • Commutative Rings. University of Chicago Press 1970.
  • Infinite Abelian Groups.
  • Fields and rings. 2nd edition 1972.
  • An introduction to differential algebra. 1957.
  • Lie algebras and locally compact groups. 1971.
  • Projective modules , Ann. of Math (2) 68 1958 372-377. (Each 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.
  • Maximal fields with valuations , Duke Math. J. 9, (1942). 303-321.


  • Donald J. Albers, GL Alexanderson, Constance Reid More Mathematical People - Contemporary Conversations , Academic Press 1994

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