February 9, 1927|
Ōbu, Aichi, Japan
|Died||August 27, 2008
|Alma mater||Nagoya University|
|Doctoral advisor||Tadasi Nakayama|
|Doctoral students||Shuzo Izumi
|Known for||Nagata ring
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.
- Nagata, Masayoshi (1960), "On the fourteenth problem of Hilbert", Proc. Internat. Congress Math. 1958, Cambridge University Press, pp. 459–462, MR 0116056
- 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
- I. P. Shestakov, & U. U. Umirbaev (2004) J. Am. Math. Soc. 17, 197–227.
- Maruyama, Masaki; Masayoshi Miyanishi; Shigefumi Mori; Tadao Oda (January 2009). "Masayoshi Nagata (1927–2008)" (PDF). Notices of the American Mathematical Society. 56 (1): 58. Retrieved 2008-12-30.
- O'Connor, John J.; Robertson, Edmund F., "Masayoshi Nagata", MacTutor History of Mathematics archive, University of St Andrews.
- Masayoshi Nagata at the Mathematics Genealogy Project