Masayoshi Nagata
{{short description|Japanese mathematician}}
{{Infobox scientist
| name = Masayoshi Nagata
| image = Masayoshi Nagata.jpg
| image_size =
| caption =
| birth_date = {{Birth date|1927|02|09|mf=y}}
| birth_place = Ōbu, Aichi, Japan
| death_date = {{Death date and age|2008|08|27|1927|02|09|mf=y}}
| death_place = Kyoto, Japan
| nationality = Japanese
| fields = Mathematics
| workplaces = Kyoto University
| alma_mater = Nagoya University
| thesis_title = Research on the 14th problem of Hilbert
| thesis_url =
| thesis_year = 1957
| doctoral_advisor = Tadasi Nakayama
| doctoral_students = Shigefumi Mori
| 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
| awards =
}}
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.
Work
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.I. P. Shestakov, & U. U. Umirbaev (2004) Journal of the American Mathematical Society 17, 197–227.
Selected works
- {{Citation | last1=Nagata | first1=Masayoshi | author1-link=Masayoshi Nagata | title=Proc. Internat. Congress Math. 1958 | chapter-url=http://mathunion.org/ICM/ICM1958/ | publisher=Cambridge University Press | mr=0116056 | year=1960 | chapter=On the fourteenth problem of Hilbert | pages=459–462 | url-status=dead | archiveurl=https://web.archive.org/web/20110717144634/http://mathunion.org/ICM/ICM1958/ | archivedate=2011-07-17 }}
- {{Citation | last1=Nagata | first1=Masayoshi | author1-link=Masayoshi Nagata | title=Lectures on the fourteenth problem of Hilbert | url=http://www.math.tifr.res.in/~publ/ln/tifr31.pdf | publisher=Tata Institute of Fundamental Research | location=Bombay | series=Tata Institute of Fundamental Research Lectures on Mathematics |mr=0215828 | year=1965 | volume=31}}
- {{citation|mr=0155856
|last=Nagata|first= Masayoshi
|title=Local rings
|series=Interscience Tracts in Pure and Applied Mathematics|volume= 13 |publisher=Interscience Publishers a division of John Wiley & Sons |place=New York-London|year= 1962| isbn=0-88275-228-6}}
References
{{reflist}}
- {{cite journal |last=Maruyama |first=Masaki |author2=Masayoshi Miyanishi |author3=Shigefumi Mori |author4=Tadao Oda |date=January 2009 |title=Masayoshi Nagata (1927–2008) |journal=Notices of the American Mathematical Society |volume=56 |issue=1 |page=58 |url=https://www.ams.org/notices/200901/tx090100056p.pdf |accessdate=2008-12-30}}
- {{MacTutor|id=Nagata}}
- {{MathGenealogy |id=99100 }}
{{Authority control}}
{{DEFAULTSORT:Nagata, Masayoshi}}
Category:20th-century Japanese mathematicians
Category:21st-century Japanese mathematicians
Category:People from Ōbu, Aichi
Category:Scientists from Aichi Prefecture
Category:Academic staff of Kyoto University