Principal Intersection Graph of Commutative Rings

Abstract

Let R be a commutative ring. The principal intersection graph of a commutative ring R, noted G_c (R), consist of all proper ideals of R as vertices. Two distinct vertices I and J are adjacent if I∩J≠0 and either I or J is a principal (cyclic) ideal. In this paper, we investigate some properties from graph theory of G_c (R) and its algebraic properties where R is a ring.