RINGS OF P-ADIC FUNCTIONS

Authors
BELAIR L
Citation
L. Belair, RINGS OF P-ADIC FUNCTIONS, The Journal of symbolic logic, 60(2), 1995, pp. 484-497
Citations number
20
Categorie Soggetti
Mathematics, Pure",Mathematics
Journal title
The Journal of symbolic logic → ACNP
ISSN journal
00224812
Volume
60
Issue
2
Year of publication
1995
Pages
484 - 497
Database
ISI
SICI code
0022-4812(1995)60:2<484:ROPF>2.0.ZU;2-I
Abstract
We study first-order properties of the quotient rings C (V)/P by a pri me ideal P, where C(V) is the ring of p-adic valued continuous definab le functions on some affine p-adic variety V. We show that they are in tegrally closed Henselian local rings, with a p-adically closed residu e field and field of fractions, and they are not valuation rings in ge neral but always satisfy For All x, y(x/y(2) V y/x(2)).