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.