On uniformlypr-ideals in commutative rings

Abstract

Let R be a commutative ring with nonzero identity and I a proper ideal of R. Then I is called a uniformly pr-ideal if there exists N ∈ N such that ab ∈ I with ann(a) = 0 then b N ∈ I. We say that the smallest N ∈ N is called order of I and denoted by ordR(I) = N. In this paper, we give some examples and characterizations of this new class of ideals.