Nagoya Mathematical Journal

On the chain problem of prime ideals

Masayoshi Nagata

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Article information

Source
Nagoya Math. J. Volume 10 (1956), 51-64.

Dates
First available in Project Euclid: 14 June 2005

Permanent link to this document
http://projecteuclid.org/euclid.nmj/1118799769

Mathematical Reviews number (MathSciNet)
MR0078974

Zentralblatt MATH identifier
0074.02503

Subjects
Primary: 09.3X

Citation

Nagata, Masayoshi. On the chain problem of prime ideals. Nagoya Math. J. 10 (1956), 51--64. http://projecteuclid.org/euclid.nmj/1118799769.


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References

  • [1] K. Oka, Sur les fonctions analytques de plusieurs variables, VIII-Lemme fondamental, J. of Math. Soc.of Japan, vol. 3 (1951), pp. 204-214.
  • [2] M. Nagata, Some remarks on local rings, Nagoya Math. J., vol. 6 (1953), pp. 53-58.
  • [2,II] M. Nagata, Some remarks on local rings, II, Memoirs Kyoto Univ., ser. A, vol. 28, No. 2 (1954), pp. 109-120.
  • [3] M. Nagata, Basic theorems on general commutative rings, Memoirs Kyoto Univ., ser. A, vol. 29, No.1 (1955), pp. 59-77.
  • [4] M. Nagata, A general theory of algebraic geometry over Dedekind domains, I, Amer. J. of Math., vol. 78, No.1 (1956), pp. 78-116.
  • [5] M. Nagata, The theory of multiplicity in general local rings, forthcoming.
  • [6] M. Nagata, The derived normal rings of Noetherian integral domains, Memoirs Kyoto Univ., ser. A, vol. 29, No.3 (1955), pp. 293-303,
  • [7] J. P. Serre, Sur la dimension homologique des anneaux et des modules noethriens, forthcoming.
  • [8] O. Zariski, Analytical irreducibility of normal varieties, Ann. of Math., vol. 49 (1948), pp. 352-361.
  • [9] O. Zariski, Sur la normalite analytique des varite normales, Ann. L'inst. Fourier, vol. 2 (1950), pp. 161-164. Mathematical Institute Kyoto University