SOME RESULTS ON A SUBGRAPH OF THE INTERSECTION GRAPH OF IDEALS OF A COMMUTATIVE RING

The rings considered in this article are commutative with identity which admit at least one nonzero proper ideal. Let R be a ring. Let us denote the collection of all proper ideals of R by I(R) and I(R){(0)} by I(R) ∗ . With R, we associate an undirected graph denoted by g(R), whose vertex set is I(R) ∗ and distinct vertices I1, I2 are adjacent in g(R) if and only if I1 ∩ I2 6= I1I2. The aim of this article is to study the interplay between the graphtheoretic properties of g(R) and the ring-theoretic properties of R.