Trivial extensions satisfying certain valuation-like properties

Abstract

In this article, we study the possible transfer of the properties of being an almost valuation ring, a pseudo-valuation ring and a pseudo-almost valuation ring between a commutative ring A and (the trivial ring extension of A arising from an A-module E). Also, we extend the notion of an almost pseudo-valuation domain to the context of arbitrary commutative rings (possibly with nontrivial zero-divisors), and we also study the possible transfer of this notion between A and . Our aim is to provide examples of new classes of commutative rings satisfying the above-mentioned properties.