Nagoya Mathematical Journal

On the theory of Henselian rings

Masayoshi Nagata

Full-text: Open access

Article information

Source
Nagoya Math. J. Volume 5 (1953), 45-57.

Dates
First available in Project Euclid: 14 June 2005

Permanent link to this document
http://projecteuclid.org/euclid.nmj/1118799392

Mathematical Reviews number (MathSciNet)
MR0051821

Zentralblatt MATH identifier
0051.02601

Subjects
Primary: 09.1X

Citation

Nagata, Masayoshi. On the theory of Henselian rings. Nagoya Mathematical Journal 5 (1953), 45--57. http://projecteuclid.org/euclid.nmj/1118799392.


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References

  • [1] Go Azumaya, On maximally central algebras, Nagoya Math. Journ. 2 (1950), pp. 119-150.
  • [2] S. Cohen– A. Seidenberg, Prime ideals and integral dependence, Bull. Amer. Math, Soc. 52 (1946), pp. 252-261,
  • [3] K. Hensel, Theorie der algebraischen Zahlen I, Teubner (1908),
  • [4] W, Krull, Allgemeine Bewertungsheorie, Jour, reine angew. Math. 167 (1932), pp. 160-196,
  • [5] W. Krull, Betrage zur Arithmetik kommutativer Integritatsbereiche III, Math. Zeit. 42 (1936-37), pp. 745-766.
  • [6] M. Nagata, On KruIs conjecture concerning valuation rings, Nagoya Math Journ. 4 (1952), pp. 29-33.
  • [7] A. Ostrowski, Untersuchungen zur arithmetischen Theorie der Krper I, Math. Zeit, 39 (1935), ppa 261-320,
  • [8] K, Rychilik, Zur Bewertungstheorie der algebraischen Krper, Journa reine angew. Math. 153 (1924), pp. 94-107.
  • [9] O. F, G. Schilling, Normal extensions of relatively complete fields, Amer. Journ. Math. 65 (1934), pp. 309-334. Mathematical Institute, Nagoya University Added in Proof, The corollary to Theorem 7 can be generalized as fol- Let D be an integrally closed quasi-local integrity domain with maximal ideal p. If o' is a Henselian integrity domain with maximal ideal pf such that o'o and p'op, then o' contains the Henselization of o up to an isomorphism over 0. This will be proved in a later paper.

See also

  • See also: Masayoshi Nagata. On the theory of Henselian rings. II. Nagoya Mathematical Journal vol. 7, (1954), pp. 1-19.
  • See also: Masayoshi Nagata. On the theory of Henselian rings. III. Mem. Coll. Sci. Univ. Kyoto. Ser. A. Math. vol. 32 (1959), pp. 93--101.