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 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 $IJ=Icap J$. We obtain some properties of this graph and study its relation to the structure of $R$.

Keywords

• graph
• diameter
• ring
• idempotent