Azumaya Gorō

Azumaya Gorō ( Japanese 東 屋 五郎 ; born February 26, 1920 in Yokohama ; † July 8, 2010 ) was a Japanese mathematician who studied algebra .

Azumaya grew up in Osaka . He studied at the University of Tokyo and received his doctorate in 1949 at Nagoya University under Iyanaga Shōkichi . He was then assistant professor at Nagoya University and from 1953 professor at Hokkaidō University . 1956 to 1959 he visited the USA, where he was two years at Yale University and one year at Northwestern University . Then he was back at the University of Hokkaido, was visiting professor at the University of Massachusetts in 1964 and at Indiana University in 1965 . From 1968 he held a full professorship at Indiana University. In 1975/76 he was visiting professor at the University of Munich and 1983/84 at the ETH Zurich .

In 1951 he introduced the Azumaya algebras named after him as a generalization of central simple algebras that are defined by rings instead of solids. He classified these algebras using Hensel's rings . Azumaya algebras found applications in algebraic geometry ( Alexander Grothendieck in the mid-1960s in his theory of the Brauer group ) and arithmetic algebraic geometry. Azumaya was mainly concerned with ring theory . An extension of the theorem of Krull - Remak - Schmidt about the unambiguous representation of a module by a direct sum of indivisible summands, which Azumaya proved in 1950, bears his name affix (Krull-Schmidt-Remak-Azumaya theorem or Krull-Schmidt-Azumaya theorem) . Independently of Kiiti Morita , he introduced the Morita duality of ring modules in the late 1950s.

He worked in Japan from the 1940s with Nakayama Tadashi , with whom he won the Chūnichi Bunkashō Prize of the Chūnichi Shimbun newspaper in 1949 . With Nakayama he also wrote a Japanese textbook on algebra.

Fonts

• with Nakayama Tadashi : 代 数学 II: 環 論 (Algebra II: ring theory), 岩 波 書店 , 1954 (Japanese)

literature

• Darrell Hale, James Osterburg (Editor): Azumaya algebras, actions, and modules. Proceedings of a conference in honor of Goro Azumaya's seventieth birthday , Contemporary Mathematics, Vol. 124, American Mathematical Society, 1992

References

1. ↑ Gorō Azumaya: On maximally central algebras (December 25, 1950), Nagoya Mathematical Journal 2, 1951, pp. 119–150 (English; Zentralblatt review )
2. ↑ Gorō Azumaya: Corrections and supplementaries to my paper concerning Krull-Remak-Schmidt's theorem (February 15, 1950), Nagoya Mathematical Journal 1, 1950, pp. 117-124 (English; Zentralblatt review ). Azumaya extended the set of R-modules of finite length to such infinite length, assuming local endomorphism rings for each addend, e.g. B. Paul Cohn : Introduction to Ring Theory , Springer, 2000, p. 83
3. ↑ Gorō Azumaya: A duality theory for injective modules. (Theory of quasi-Frobenius modules) , American Journal of Mathematics 81, January 1959, pp. 249–278 (English; Zentralblatt review )
4. ↑ The award is given annually to five people from the Nagoya region who have distinguished themselves in science and the arts

Japanese name: As is common in Japan, the family name comes before the first name in this article . Thus Azumaya is the family name, Gorō the first name.