$I$-prime ideals

Abstract

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 ∈ R with ab ∈ P − IP implies either a ∈ P or b ∈ 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.