A GRAPH WHICH RECOGNIZES IDEMPOTENTS OF A COMMUTATIVE RING

Abstract

In 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 $R$.