Some classes of perfect annihilator-ideal graphs associated with commutative rings

Abstract

Let $R$ be a commutative ring and let $Bbb A(R)$ bethe set of all ideals of $R$ with nonzero annihilator.The annihilator-ideal graph of $R$ is defined as the graph${A_I}(R)$ with the vertex set $Bbb A(R)^*=Bbb A(R)setminus{0}$ and twodistinct vertices $I$ and $J$ are adjacent if and only if${rm Ann}_R(IJ)neq{rm Ann}_R(I) cup{rm Ann}_R(J)$. In this paper, perfectness of${A_I}(R)$ for some classes of rings is investigated.