University of GuilanJournal of Algebra and Related Topics2345-39316220181201Some results on a subgraph of the intersection graph of ideals of a commutative ring3561332810.22124/jart.2018.11188.1114ENS. VisweswaranDepartment of Mathematics,
Saurashtra University, Rajkot, India.P. VadhelDepartment of Mathematics,
Saurashtra University, Rajkot, IndiaJournal Article20180831The 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 $mathbb{I}(R)$ and $mathbb{I}(R)backslash {(0)}$ by $mathbb{I}(R)^{*}$. With $R$, we associate an undirected graph denoted by $g(R)$, whose vertex set is $mathbb{I}(R)^{*}$ and distinct vertices $I_{1}, I_{2}$ are adjacent in $g(R)$ if and only if $I_{1}cap I_{2}neq I_{1}I_{2}$. The aim of this article is to study the interplay between the graph-theoretic properties of $g(R)$ and the ring-theoretic properties of $R$.https://jart.guilan.ac.ir/article_3328_37da989245b3ff3ca164523e990de30b.pdf