%0 Journal Article
%T Some results on a subgraph of the intersection graph of ideals of a commutative ring
%J Journal of Algebra and Related Topics
%I University of Guilan
%Z 2345-3931
%A Visweswaran, S.
%A Vadhel, P.
%D 2018
%\ 12/01/2018
%V 6
%N 2
%P 35-61
%! Some results on a subgraph of the intersection graph of ideals of a commutative ring
%K Artinian ring
%K Special principal ideal ring
%K diameter
%K girth
%K clique number
%R 10.22124/jart.2018.11188.1114
%X 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 $mathbb{I}(R)$ 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 $R$.
%U https://jart.guilan.ac.ir/article_3328_37da989245b3ff3ca164523e990de30b.pdf