## Journal of Symbolic Logic

### Anneaux de Fonctions $p$-Adiques

Luc Belair

#### Abstract

We study first-order properties of the quotient rings $\mathscr{C}(V)/\mathscr{P}$ by a prime ideal $\mathscr{P}$, where $\mathscr{C}(V)$ 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 $\forall x, y(x|y^2 \vee y|x^2)$.

#### Article information

Source
J. Symbolic Logic, Volume 60, Issue 2 (1995), 484-497.

Dates
First available in Project Euclid: 6 July 2007

https://projecteuclid.org/euclid.jsl/1183744748

Mathematical Reviews number (MathSciNet)
MR1335129

Zentralblatt MATH identifier
0868.03017

JSTOR
Belair, Luc. Anneaux de Fonctions $p$-Adiques. J. Symbolic Logic 60 (1995), no. 2, 484--497. https://projecteuclid.org/euclid.jsl/1183744748