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Additional resources for Algebraic Geometry and Commutative Algebra. In Honor of Masayoshi Nagata, Volume 2

Sample text

Then A is also quasi-excellent. Ideal-adic Completion of Noetherian Rings II 455 Notation. In this note, all rings are commutative with 1. Standard notation and terminology are those of Bourbaki[2], EGA[5], Matsumura[12] and Nagata[13]. We also use the same terminology as in [16] except: a universally Japanese ring is called here a nagata ring. , — For a local ring (A, m), we say P ( A ) is true ("P(A) holds", or simply P(>1)), when A have the property P . 1. Let Ay Β be noetherian rings. 2) P((B ®A k')P>) is true for any p G Spec(^l) and any P' G Spec(ß <8U k') of any finite extension field k' over κ(ρ).

79 (1964), 109-326. J. Marot, Sur les anneaux universellement japonais, Bull. Soc. Math. France 103 (1975), 103-111. J. Marot, P-rings and P-homomorphisms, J. Alg. 87 (1984), 136-149. J. Marot, Sur la complété adique d'un anneau excellent, preprint. H. Matsumura, Commutative Algebra, Benjamin 1970 (sec. ed. 1980). M . Nagata, Local Rings, John Willey 1962 (rep. ed. Krieger 1975). M . Nagata, Imbedding of an abstract variety in a complete variety, J. Math. Kyoto Univ. 2 (1962), 1-10. J. Nishimura, Note on Krull domains, J.

Math. France 103 (1975), 103-111. J. Marot, P-rings and P-homomorphisms, J. Alg. 87 (1984), 136-149. J. Marot, Sur la complété adique d'un anneau excellent, preprint. H. Matsumura, Commutative Algebra, Benjamin 1970 (sec. ed. 1980). M . Nagata, Local Rings, John Willey 1962 (rep. ed. Krieger 1975). M . Nagata, Imbedding of an abstract variety in a complete variety, J. Math. Kyoto Univ. 2 (1962), 1-10. J. Nishimura, Note on Krull domains, J. Math. Kyoto Univ. 15 (1975), 397-400. J. Nishimura, On ideal-adic completion of noetherian rings, J.

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