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A Note on Henselian Valuation Rings

Published online by Cambridge University Press:  20 November 2018

Otto Endler
Otto Endler*
Affiliation:
Mathematisches Institut der, Universitat Bonn (Germany)
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Let K be a field and Ka its algebraic closure. A valuation a ring A of K is called henselian, if there is only one valuation ring C of Ka which lies over A (i.e. such that C ∩ K = A) or, equivalently, if Hensel's Lemma is valid for K, A (see [5], F). In the following, we shall consider only rank one valuation rings.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 11 , Issue 2 , June 1968 , pp. 185 - 189
Copyright
Copyright © Canadian Mathematical Society 1968

References

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2. Endler, O., Bewertungstheorie, . Unter Benutzung einer Vorlesung von W. Krull. (vol. I, II). (Bonner Math. Schriften Nr. 15, 1963).Google Scholar
3. Kaplansky, I. and Schilling, O.F.G., Some remarks on relatively complete fields. Bull. Amer. Math. Soc. 48 (1942), 744-747.Google Scholar
4. Ribenboim, P., A short note on henselian fields. Math. Ann. 173 (1967), 83-88.Google Scholar
5. Ribenboim, P., Théorie des valuations. (Sém. Math. Sup., Univ. Montréal, 1964).Google Scholar