A NOTE ON THE INTERSECTION GRAPHS OF IDEALS OF RINGS

Let R be a ring with unity and I(R) ∗ be the set of all nontrivial ideals of R. The intersection graph of ideals of R is the graph G(R) with vertices I(R) ∗ , and two distinct vertices I and J are adjacent if and only if I ∩ J 6= 0. Let M be a unitary R-module. The M-intersection graph of ideals of R, denoted by G M (R), is a graph with the vertex set I(R) ∗ , and two distinct vertices I and J are adjacent if and only if IM ∩ JM 6= 0. In this note, we investigate some properties of G M (R).