Gr-(2, n)-ideals in graded commutative rings

Abstract

Let G be a group with identity e and let R be a G-graded ring. In this paper, we introduce and study the concept of graded (2, n)-ideals of R. A proper graded ideal I of R is called a graded (2, n)-ideal of R if whenever rst is an element of I where r, s, t is an element of h(R), then either rt is an element of I or rs is an element of Gr(0) or st is an element of Gr(0). We introduce several results concerning gr-(2, n)-ideals. For example, we give a characterization of graded (2, n)-ideals and their homogeneous components. Also, the relations between graded (2, n)-ideals and others that already exist, namely, the graded prime ideals, the graded 2-absorbing primary ideals, and the graded n-ideals are studied.