Shahrood University of TechnologyJournal of Algebraic Systems2345-51287220200101A GRAPH WHICH RECOGNIZES IDEMPOTENTS OF A COMMUTATIVE RING143154158510.22044/jas.2019.7405.1365ENH.DorbidiDepartment of Mathematics, Faculty of Science, University of Jiroft, P.O. Box
78671-61167, Jiroft, Iran.S.AlikhaniDepartment of Mathematics, Yazd University, 89195-741, Yazd, Iran.Journal Article20180827In this paper we introduce and study a graph on the set of ideals of a<br /> commutative ring $R$. The vertices of this graph are non-trivial ideals of $R$ and<br /> two distinct ideals $I$ and $J$ are adjacent if and only $IJ=Icap J$. We<br /> obtain some properties of this graph and study its<br /> relation to the structure of $R$.http://jas.shahroodut.ac.ir/article_1585_0115d6f468b7fb69d3639428ff331638.pdf