A GRAPH WHICH RECOGNIZES IDEMPOTENTS OF A COMMUTATIVE RING

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