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Anneaux de fonctions p-adiques

Published online by Cambridge University Press:  12 March 2014

Luc Bélair
Luc Bélair*
Affiliation:
Département de Mathématiques, Université du Québec à Montréal, Montréal, Québec H3C 3P8, Canada, E-mail: [email protected]
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Abstract

We study first-order properties of the quotient rings (V)/ by a prime ideal where (V) is the ring of p-adic valued continuous definable functions on some affine p-adic variety V. We show that they are integrally closed Henselian local rings, with a p-adically closed residue field and field of fractions, and they are not valuation rings in general but always satisfy ∀ x, y(x∣y2 ∨ y∣x2).

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 60 , Issue 2 , June 1995 , pp. 484 - 497
Copyright
Copyright © Association for Symbolic Logic 1995

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