Masayoshi Nagata

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Masayoshi Nagata
Born (1927-02-09)February 9, 1927
Ōbu, Aichi, Japan
Died August 27, 2008(2008-08-27) (aged 81)
Kyoto
Nationality Japanese
Alma mater Nagoya University
Known for Nagata ring
Nagata–Biran conjecture
Scientific career
Fields Mathematics
Institutions Kyoto University
Doctoral advisor Tadasi Nakayama
Doctoral students Shigefumi Mori

Masayoshi Nagata (Japanese: 永田 雅宜 Nagata Masayoshi; February 9, 1927 – August 27, 2008) was a Japanese mathematician, known for his work in the field of commutative algebra.

Nagata's compactification theorem shows that varieties can be embedded in complete varieties. The Chevalley–Iwahori–Nagata theorem describes the quotient of a variety by a group.

He found counterexamples to several open mathematical questions. In 1959 he introduced a counterexample to the general case of Hilbert's fourteenth problem on invariant theory. His 1962 book on local rings contains several other counterexamples he found, such as a commutative Noetherian ring that is not catenary, and a commutative Noetherian ring of infinite dimension.

Nagata's conjecture on curves concerns the minimum degree of a plane curve specified to have given multiplicities at given points; see also Seshadri constant. Nagata's conjecture on automorphisms concerns the existence of wild automorphisms of polynomial algebras in three variables. Recent work has solved this latter problem in the affirmative.[1]

Selected works[edit]

  • Nagata, Masayoshi (1960), "On the fourteenth problem of Hilbert", Proc. Internat. Congress Math. 1958, Cambridge University Press, pp. 459–462, MR 0116056, archived from the original on 2011-07-17
  • Nagata, Masayoshi (1965), Lectures on the fourteenth problem of Hilbert (PDF), Tata Institute of Fundamental Research Lectures on Mathematics, 31, Bombay: Tata Institute of Fundamental Research, MR 0215828
  • Nagata, Masayoshi (1962), Local rings, Interscience Tracts in Pure and Applied Mathematics, 13, New York-London: Interscience Publishers a division of John Wiley & Sons , ISBN 0-88275-228-6, MR 0155856

References[edit]

  1. ^ I. P. Shestakov, & U. U. Umirbaev (2004) J. Am. Math. Soc. 17, 197–227.