A GRAPH WHICH RECOGNIZES IDEMPOTENTS OF A COMMUTATIVE RING

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

I J = I \cap J

. We
obtain some properties of this graph and study its
relation to the structure of

R

Keywords