# Masayoshi Nagata

**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 | |
---|---|

Born | |

Died | August 27, 2008 81) | (aged

Nationality | Japanese |

Alma mater | Nagoya University |

Known for | Nagata ring Nagata's conjecture Nagata's conjecture on curves Nagata–Biran conjecture |

Scientific career | |

Fields | Mathematics |

Institutions | Kyoto University |

Doctoral advisor | Tadasi Nakayama |

Doctoral students | Shigefumi Mori |

## Work

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.

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

- 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

- 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