George Whaples

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George William Whaples , (born November 27, 1914 in Neponset , Illinois , † May 2, 1982 in Amherst (Massachusetts) ) was an American mathematician.

Whaples received his bachelor's degree from Knox College in 1935 and received his PhD under Mark Hoyt Ingraham at the University of Wisconsin in 1939 ( On the Structure of Modules with a Commutative Algebra as Operator Domain ). Ingraham thought he was one of the toughest math students the University of Wisconsin had ever had and compared him to his own teacher, EH Moore . As a post-doctoral student he was at Indiana University from 1939 to 1941 with Emil Artin , with whom he researched class field theory . In 1942/43 he was Hermann Weyl's assistant at the Institute for Advanced Study . He was then at Indiana University, where he became a professor in 1958 and was professor at the University of Massachusetts at Amherst from 1966 .

At times he was also on the faculties of the University of Wisconsin , Johns Hopkins University , the University of Pennsylvania and the University of Notre Dame .

In the 1940s he and Artin characterized global fields ( algebraic number fields and function fields ) axiomatically with the help of valuation theory through the validity of the product formula (Artin therefore called them PF fields in his book Algebraic Numbers and Algebraic Functions from 1967). These were exactly the bodies to which class field theory could be applied. Artin and Whaples complained in the introduction to their 1946 article that the foundations of class field theory were derived from two simple axioms. They also introduced the ring of valuation vectors of global bodies, noting that the idels of Claude Chevalley (introduced by him in 1936) formed a multiplicative subgroup. The ring of evaluation vectors was named in 1959 by André Weil Adelring .

In a 1943 paper with Artin, he treated simple rings (and applied results from the theory of simple algebras to these), thereby simplifying the proof of Wedderburn's theorem . In 1942 he gave a simplified proof of a theorem by Wilhelm Grunwald .

He is buried in the Shutesbury Jewish Cemetery, Franklin County, Massachusetts.

He was one of the editors of the Duke Mathematical Journal and the Proceedings of the American Mathematical Society, in whose council he was from 1962 to 1965.

Fonts

  • with Artin: The theory of simple rings, Amer. J. Math., Vol. 65, 1943, pp. 87-107
  • with Artin: Axiomatic characterization of fields by the product formula for valuations, Bulletin Am. Math. Soc., Volume 51, 1945, pp. 469-492
  • with Artin: A note on axiomatic characterization of fields, Bull. Amer. Math. Soc., Vol. 52, 1946, pp. 245-247
  • Non-analytic class field theory and Grunwald's theorem, Duke Mathematical Journal, Volume 9, 1942, pp. 455-473

literature

  • Della Dumbaugh, Joachim Schwermer : The collaboration of Emil Artin and George Whaples: Artin's mathematical circle extends to America, Archive History Exact Sciences, Volume 66, 2012, pp. 465-484

Individual evidence

  1. ↑ Life data in the obituary in the Notices of the Am. Math. Soc., August 1981, p. 430
  2. ↑ Weil, Adèles et groupes algébriques, Seminaire Bourbaki No. 186
  3. ^ Find a Grave
personal data
SURNAME Whaples, George
ALTERNATIVE NAMES Whaples, George William (full name)
BRIEF DESCRIPTION American mathematician
DATE OF BIRTH November 27, 1914
PLACE OF BIRTH Neponset (Illinois)
DATE OF DEATH May 2, 1982
Place of death Amherst, Massachusetts