Anneaux de Fonctions $p$-Adiques
Belair, Luc
J. Symbolic Logic, Tome 60 (1995) no. 1, p. 484-497 / Harvested from Project Euclid
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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 $\forall x, y(x|y^2 \vee y|x^2)$.
Publié le : 1995-06-14
Classification:  
@article{1183744748,
     author = {Belair, Luc},
     title = {Anneaux de Fonctions $p$-Adiques},
     journal = {J. Symbolic Logic},
     volume = {60},
     number = {1},
     year = {1995},
     pages = { 484-497},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/1183744748}
}

Belair, Luc. Anneaux de Fonctions $p$-Adiques. J. Symbolic Logic, Tome 60 (1995) no. 1, pp.  484-497. http://gdmltest.u-ga.fr/item/1183744748/