I-prime ideals

In this paper, we introduce a new generalization of weakly prime ideals called I-prime. Suppose R is a commutative ring with identity and I a fixed ideal of R. A proper ideal P of R is I-prime if for a, b \in R with ab \in P-IP implies either a \in P or b \in P. We give some characterizations of I-prime ideals and study some of its properties.  Moreover, we give conditions  under which I-prime ideals becomes prime or weakly prime and we construct the view of I-prime ideal in decomposite rings.

Keywords:

prime ideal , weakly prime ideal , almost prime ideal , radical of the ideal