Planarity of a spanning subgraph of the intersection graph of ideals of a commutative ring II, Quasilocal Case

Abstract

The rings we consider in this article are com- mutative with identity 1 6= 0 and are not fields. Let R be a ring.

We denote the collection of all proper ideals of R by I(R) and the collection I(R) \ {(0)} by I(R) ∗ . Let H(R) be the graph associated

with R whose vertex set is I(R)

∗ and distinct vertices I, J are adja- cent if and only if IJ 6= (0). The aim of this article is to discuss the

planarity of H(R) in the case when R is quasilocal.