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Smoothness of Noetherian rings

Published online by Cambridge University Press:  22 January 2016

Hiroshi Tanimoto
Hiroshi Tanimoto*
Affiliation:
Department of Mathematics Faculty of Science, Nagoya University, Chikusa-ku, Nagoya 464, Japan
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In [16] we studied the following problems which had been asked by H. Matsumura (cf. [11]):

  • (I) What is the difference between smoothness and J-smoothness? In particular, concerning the characterization of smoothness,

  • (II) When is a ring A[X1 …, Xn]/a smooth over A?

In this paper, according to these problems, we will study J-smoothness further when rings are noetherian as in [16].

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 95 , September 1984 , pp. 163 - 179
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1984

References

[ 1 ] André, M., Homologie des algebres commutatives, Springer, 1974.CrossRefGoogle Scholar
[ 2 ] André, M., Localisation de la lissité formelle, Manuscripta Math., 13 (1974), 297–307.CrossRefGoogle Scholar
[ 3 ] Brezuleanu, A., Smoothness and regularity, Compositio Math., 24 (1972), 1–10.Google Scholar
[ 4 ] Brezuleanu, A. and Radu, N., Excellent rings and good separation of the module of differentials, Rev. Roummaine Math. Pures Appl., 23 (1978), 1455–1470.Google Scholar
[ 5 ] Greco, S., Two theorems on excellent rings, Nagoya Math. J., 60 (1976), 139–149.CrossRefGoogle Scholar
[ 6 ] Grothendieck, A., Éléments de Géométrie Algébrique, Ch. IV, Publ. IHES no. 20 (1964), no. 24 (1965), no. 32 (1967).Google Scholar
[ 7 ] Kunz, E., On noetherian rings of characteristic p, Amer. J. Math., 98 (1976), 999-1013.CrossRefGoogle Scholar
[ 8 ] Marot, J., Limite inductive plate de P-anneaux, J. Algebra, 57 (1979), 484–496.CrossRefGoogle Scholar
[ 9 ] Matsumura, H., Quasi-coefficient rings of a local ring, Nagoya Math. J., 68 (1977), 123–130.CrossRefGoogle Scholar
[10] Matsumura, H., Commutative Algebra, second edition, Benjamin, 1980.Google Scholar
[11] Matsumura, H., Commutative Rings (in Japanese), Kyoritsu, Tokyo 1980.Google Scholar
[12] Nagata, M., Local Rings, Interscience, 1962.Google Scholar
[13] Nishimura, J., On ideal-adic completion of noetherian rings, J. Math. Kyoto Univ., 21 (1981), 153–169.Google Scholar
[14] Seydi, H., Sur la théorie des anneaux excellents en caractéristique p, Bull. Soc. Math. France, 96 (1972), 193–198.Google Scholar
[15] Tanimoto, H., On the base field chane of P-rings and P-2 rings, Nagoya Math. J., 90 (1983), 77–83.CrossRefGoogle Scholar
[16] Tanimoto, H., Some characterizations of smoothness, J. Math. Kyoto Univ., 23 (1983), 695–706.Google Scholar