Graded 2r-Ideals
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graded r-ideal, graded pr-ideal, graded uniformly pr-idealAbstract
Let G be a group and R be a commutative G-graded ring with nonzero unity. In this article, we establish the concept of graded 2r-ideals, which lies somewhere between graded r-ideals and graded uniformly pr-ideals. A proper graded ideal P of R is said to be a graded 2r-ideal of R if whenever x, y ∈ h(R) such that xy ∈ P , then either x2 ∈ P or y ∈ zd(R), where zd(R) is the set of all zero divisors of R. Several properties of graded 2r-ideals have been achieved, and various results have been investigated.
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