Tadashi Nakayama (mathematician)

Tadashi Nakayama, also Tadasi Nakayama, Tadasi Nakamura (Japanese中山 正, Tadashi Nakayama, born July 26, 1912 in the prefecture of Tokyo, † June 5, 1964 in Nagoya ) was a Japanese mathematician who worked on algebra.

Life and work

Tadashi Nakayama made ​​in 1935 graduated from the University of Tokyo. Algebra it seems self-study of the book of Emmy Noether student Kenjiro Shoda to have learned. In 1935 he was researcher and assistant professor in 1937 at the University of Osaka. 1937 to 1939 he was at Princeton, where he met Richard Brauer, Emil Artin, Claude Chevalley and Cecil J. Nesbitt at the Institute for Advanced Study. In particular, he was influenced by Brauer, whom he visited twice in Toronto and was leading him to the study of the representation theory. In 1941 he received his doctorate at the University of Osaka. In 1942 he was assistant professor and in 1944 professor at the University of Nagoya. 1948/49, he was at the University of Illinois, from 1953 to 1955 at the University of Hamburg and 1955/56, again at the Institute for Advanced Study. He died of tuberculosis disease, which he had already before 1937, but at that time concealed in order to travel abroad can.

Nakayama worked on modular representations of the symmetric groups, Galois theory of rings and quasi- Frobenius rings. He was also interested in class field theory ( 1952, he led there by Gerhard Hochschild a cohomology a ) and is said to have incorporated in the years before his death intensely in the revolutionary innovations of algebraic geometry by Alexander Grothendieck and his school, what his health deteriorated. According to him, the lemma of Nakayama is named in commutative algebra.

With Gorō Azumaya he wrote a book on advanced algebra, in which they represented many of its results.

In 1949 he won with his scientific collaborator Gorō Azumaya the price Chunichi Bunkashō the newspaper Chunichi Shimbun. In 1954 he won the prize of the Japanese Academy of Sciences Nippon Gakushiin - shō. From 1963 he was a member of the Japanese Academy of Sciences.

Writings

  • 局 所 类 体 论( Local class field theory ) ,岩 波 书店, 1935 (in Japanese )
  • 束 论( lattice theory ) ,岩 波 书店, 1944 (in Japanese )
  • 代数 系 と 微分:代 数学 より の 二 三 の 話題( Algebraic structure and derivation ) ,河 出 书房, 1948 ( Japanese)
  • 集合· ·位相代数 系(quantity, topology, algebraic structure)至 文 堂, 1949 (in Japanese )
  • With Gorō Azumaya :代 数学II:环 论( Algebra II: Ring Theory ) ,岩 波 书店, 1954 (in Japanese )
  • With Akira Hattori:ホモロジー 代 数学( homological algebra) ,共 立 出版, 1957 ( Japanese)

Article

  • A theorem on p- adic skew-field (12 April 1934), Proceedings of the Imperial Academy 10, 1934, pp. 198-199, doi: 10.3792/pia/1195580638
  • Kenjiro Shoda with: About the product of two algebra classes with mutually prime discriminants (12 October 1934), Proceedings of the Imperial Academy 10, 1934, pp. 443-446, doi: 10.3792/pia/1195580561
  • About the definition of Shodaschen discriminant of a normal simple hypercomplex system (12 October 1934), Proceedings of the Imperial Academy 10, 1934, pp. 447-449, doi: 10.3792/pia/1195580562
  • A remark on representations of groups (30 October 1937), Bulletin of the AMS 44, 1938, pp. 233-235, doi: 10.1090/S0002-9904-1938-06723-7 (English)
  • Cecil J. Nesbitt: Note on symmetric algebras (21 March 1938), Annals of Mathematics 39, July 1938, pp. 659-668 (English)
  • On Frobeniusean algebras (English; dissertation) I (2 February 1939), Annals of Mathematics 40, July 1939, pp. 611-633, doi: 10.2307/1968946
  • II (13 July 1939), Annals of Mathematics 42, January 1941, pp. 1-21, doi: 10.2307/1968984
  • III (13 June 1941), Japanese Journal of Mathematics 18, 1942, pp. 49-65
Princeton (New Jersey) Nakayama lemma Digital Object Identifier
591280
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