ON THE EXTENSIONS OF A DISCRETE VALUATION IN A NUMBER FIELD

El Fadil, Lhoussain and Deajim, Abdulaziz ON THE EXTENSIONS OF A DISCRETE VALUATION IN A NUMBER FIELD. 1222. ISSN 12445 (Unpublished)

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Abstract

Let K be a number �eld de�ned by a monic irreducible polynomial F(X) 2 Z[X] and p a �xed rational prime. Assume that F(X) factors modulo p into the product of powers of r distinct monic irreducible polynomials, and let �p be the discrete valuation associated to p. We present in this paper a condition, weaker than the known ones, which guarantees the existence of exactly r valuations of K extending �p. We further specify the rami�cation indices and residue degrees of these extended valuations in such a way that generalizes the known estimates. Some useful remarks and computational examples are also given to highlight some improvements due to our result. 1. Introduction

Item Type: Article
Subjects: Mathematics
Divisions: College of Sciences > Mathematics
Depositing User: LHOUSSAIN EL FADIL
Date Deposited: 07 Mar 2016 03:54
Last Modified: 07 Mar 2016 03:54
URI: http://eprints.kku.edu.sa/id/eprint/260

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