Commutative Coherent Rings

Abstract

Throughout this paper R will be a commutative ring with 1. The purpose of this paper is to provide two new characterizations of coherent rings. The first of these characterizations shows that the class of coherent rings is precisely the class of rings for which certain duality homomorphisms are isomorphisms. And the second of these characterizations shows that the class of coherent rings is precisely the class of rings for which the endomorphism ring of any infective module is a flat module. We can show as a consequence that the endomorphism ring of a universal infective R -module is a faithfully flat R -module whenever R is a coherent ring.