GRADED UNIFORMLY pr-IDEALS

Abstract

Let R be a G-graded commutative ring with a nonzero unity and P be a proper graded ideal of R. Then P is said to be a graded uniformly pr-ideal of R if there exists n ∈ N such that whenever a, b ∈ h(R) with ab ∈ P and Ann(a) = {0}, then bn ∈ P . The smallest such n is called the order of P and is denoted by ordR(P ). In this article, we study the characterizations on this new class of graded ideals, and investigate the behaviour of graded uniformly pr-ideals in graded factor rings and in direct product of graded rings.