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.