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 commutative with identity 1 ≠ 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 adjacent if and only if IJ ≠ (0). The aim of this article is to discuss the planarity of H(R) in the case when R is quasilocal.