On the theory of Henselian rings

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On the theory of Henselian rings

Masayoshi Nagata

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

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See also: Masayoshi Nagata. On the theory of Henselian rings. II. Nagoya Mathematical Journal vol. 7, (1954), pp. 1-19.

Project Euclid: euclid.nmj/1118799554

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.

Mathematical Reviews (MathSciNet): MR0109835

Primary Subjects: 09.1X

Full-text: Open access

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Permanent link to this document: http://projecteuclid.org/euclid.nmj/1118799392
Mathematical Reviews number (MathSciNet): MR0051821
Zentralblatt MATH identifier: 0051.02601

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References

[1] Go Azumaya, On maximally central algebras, Nagoya Math. Journ. 2 (1950), pp. 119-150.

Mathematical Reviews (MathSciNet): MR12:669g

Zentralblatt MATH: 0045.01103

Project Euclid: euclid.nmj/1118764746

[2] S. Cohen– A. Seidenberg, Prime ideals and integral dependence, Bull. Amer. Math, Soc. 52 (1946), pp. 252-261,

Mathematical Reviews (MathSciNet): MR7:410a

Zentralblatt MATH: 0060.07003

Digital Object Identifier: doi:10.1090/S0002-9904-1946-08552-3

Project Euclid: euclid.bams/1183507841

[3] K. Hensel, Theorie der algebraischen Zahlen I, Teubner (1908),

Zentralblatt MATH: 39.0269.01

[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.

Mathematical Reviews (MathSciNet): MR13:904a

Zentralblatt MATH: 0046.25702

Project Euclid: euclid.nmj/1118799310

[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.

Mathematical Reviews (MathSciNet): MR5:88g

Zentralblatt MATH: 0061.05603

Digital Object Identifier: doi:10.2307/2371818

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Nagoya Mathematical Journal

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