Document Type: Original Manuscript

Authors

1 Department of Mathematics, Faculty of Science, University of Jiroft, P.O. Box 78671-61167, Jiroft, Iran.

2 Department of Mathematics, Yazd University, 89195-741, Yazd, Iran.

Abstract

In this paper we introduce and study a graph on the set of ideals of a
commutative ring $R$. The vertices of this graph are non-trivial ideals of $R$ and
two distinct ideals $I$ and $J$ are adjacent if and only $IJ=I\cap J$. We
obtain some properties of this graph and study its
relation to the structure of $R$.

Keywords