n-X-COHERENT RINGS

Year 2010, Volume: 7 Issue: 7, 128 - 139, 01.06.2010

Driss Bennis

Abstract

This paper unifies several generalizations of coherent rings in one notion. Namely, we introduce n-X -coherent rings, where X is a class of modules and n is a positive integer, as those rings for which the subclass Xn of n-presented modules of X is not empty, and every module in Xn is n + 1-presented. Then, for each particular class X of modules, we find correspondent relative coherent rings. Our main aim is to show that the well-known Chase’s, Cheatham and Stone’s, Enochs’, and Stenstr¨om’s characterizations of coherent rings hold true for any n-X -coherent rings.

Keywords

n-X -coherent rings, n-X -flat modules, n-X -injective modules, Charter modules, preenvelopes

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• Department of Mathematics Faculty of Science and Technology of Fez, Box 2202
• University S. M. Ben Abdellah Fez, Morocco e-mail: driss [e-mail]