Resumen de Annihilator-Semigroups and Rings

D. D. Anderson, Sangmin Chun

• 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, ·) is a multiplicative subsemigroup of (R, ·) with the property that for each r in R there exists a unique s in S with 0 : r = 0 : s. The quotient monoid R/~ where a ~ b if and only if 0 : a = 0 : b is called the annihilator congruence semigroup of R. If S is an annihilator-semigroup for R, then S is isomorphic to R/~. In this paper we investigate annihilator-semigroups, annihilator congruence semigroups, and annihilator-semigroup rings