Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-11-22T06:49:14.467Z Has data issue: false hasContentIssue false
  • English
  • Français

On the Theory of Henselian Rings

Published online by Cambridge University Press:  22 January 2016

Masayoshi Nagata
Masayoshi Nagata*
Affiliation:
Mathematical Institute, Nagoya University
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The notion of Henselian rings was introduced by G. Azuma-ya [l]. We concern ourselves in the present paper mainly with Henselizations of integrally closed integrity domains. Chapter I deals with general integrally closed integrity domains. As a preparation of our studies, we introduce the notion of decomposition rings analogously as in the case of fields (§1). And then we define the notions of (local) Henselian rings and Henselizations of integrally closed integrity domains, and obtain several results concerning characterizations of Henselian rings and the uniqeness of Henselizations (§2).

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 5 , February 1953 , pp. 45 - 57
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1953

References

[1] Azumaya, Go, On maximally central algebras, Nagoya Math. Journ. 2 (1950), pp. 119–150.CrossRefGoogle Scholar
[2] Cohen, I. S. — Seidenberg, A., Prime ideals and integral dependence, Bull. Amer. Math, Soc. 52 (1946), pp. 252–261.CrossRefGoogle Scholar
[3] Hensel, K., Theorie der algebraischen Zahlen I, Teubner (1908).Google Scholar
[4] Krull, W., Allgemeine Bewertungstheorie, Jour, reine angew. Math. 167 (1932), pp. 160–196.CrossRefGoogle Scholar
[5] Krull, W., Beiträge zur Arithmetik kommutativer Integritätsbereiche III, Math. Zeit. 42 (1936-37), pp. 745–766.CrossRefGoogle Scholar
[6] Nagata, M., On Krull’s conjecture concerning valuation rings, Nagoya Math. Journ. 4 (1952), pp. 29–33.CrossRefGoogle Scholar
[7] Ostrowski, A., Untersuchungen zur arithmetischen Theorie der Körper I, Math. Zeit, 39 (1935), pp. 261–320.Google Scholar
[8] Rychilik, K., Zur Bewertungstheorie der algebraischen Körper, Journ. reine angew. Math. 153 (1924), pp. 94–107.CrossRefGoogle Scholar
[9] Schilling, O. F. G., Normal extensions of relatively complete fields, Amer. Journ. Math. 65 (1934), pp. 309–334.Google Scholar