Annihilator-semigroup rings

Abstract

Let $R$ be a commutative ring with 1. We define $R$ to be an annihilator-semigroup ring if $R$ has an annihilator-Semigroup $S$, that is, $(S, \cdot)$ is a multiplicative subsemigroup of $(R, \cdot)$ with the property that for each $r \in R$ there exists a unique $s \in S$ with $0 : r = 0 : s$. In this paper we investigate annihilator-semigroups and annihilator-semigroup rings.