n-X-COHERENT RINGS

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International Electronic Journal of Algebra
Volume:7 Issue:7
n-X-COHERENT RINGS

n-X-COHERENT RINGS

Authors : Driss BENNİS

Pages : 128-139

View : 18 | Download : 12

Publication Date : 2010-06-01

Article Type : Research Paper

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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