On graded j-ideals over graded rings

Abstract

. The goal of this article is to present the graded J-ideals of G-graded rings which are extensions of J-ideals of commutative rings. A graded ideal P of a G-graded ring R is a graded J-ideal if whenever x, y & ISIN; h(R), if xy & ISIN; P and x & ISIN;̸ J(R), then y & ISIN; P, where h(R) and J(R) denote the set of all homogeneous elements and the Jacobson radical of R, respectively. Several characterizations and properties with supporting examples of the concept of graded J-ideals of graded rings are investigated.