Commutative Ring Theory

3 The Graded and Tame Extensions

M. BOULAGOUAZ Département de Mathématiques et d’Informatique, Faculté des Sciences de Fès, Université de Fès, B.P. 1796 Atlas Fès, Morocco

1. Introduction

Every valuation on a field k defines a filtration of this field. The graded ring $gr(k)$ associated to this filtration has the property that all homogeneous non-zero elements are invertible; such a ring is called graded field. The idea of using this kind of construction to study valuated fields is due to M.Krasner [8] who prefers to study the set of homogeneous elements of the graded ring, rather than the graded ring itself.

The main point of this article is to show how certain properties of some extension of valuated fields can be translated in terms of the ...