On the dominating sets of the complement of the annihilating ideal graph of a commutative ring

Abstract

Let R be a commutative ring with identity which is not an integral domain. Let A(R)∗ denote the collection of all nonzero annihilating ideals of R and AG(R) denote the annihilating ideal graph of R. In this article, we consider the dominating sets of (AG(R))c (where (AG(R))c is the complement of AG(R)) and study the influence of the dominating sets of (AG(R))c on the ring structure of R and vice-versa.