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.
Masayoshi Nagata | |
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Born | |
Died | August 27, 2008 Kyoto, Japan | (aged 81)
Nationality | Japanese |
Alma mater | Nagoya University |
Known for | Nagata ring Nagata's conjecture Nagata's conjecture on curves Nagata's compactification theorem Chevalley–Iwahori–Nagata theorem Zariski–Nagata purity Mori–Nagata theorem Analytically irreducible ring |
Scientific career | |
Fields | Mathematics |
Institutions | Kyoto University |
Thesis | Research on the 14th problem of Hilbert (1957) |
Doctoral advisor | Tadasi Nakayama |
Doctoral students | Shigefumi Mori |
Nagata's compactification theorem shows that algebraic varieties can be embedded in complete varieties. The Chevalley–Iwahori–Nagata theorem describes the quotient of a variety by a group.
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]