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 ∈ 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.