2021/04/12 by Rashid Abu-Dawwas, Abu-Dawwas, Rashid, Malik Bataineh +3
Mathematics · #13A02 #16W50 #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2104.05140
openalex publication_date 2021/04/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this article, we introduce a generalization of the concept of graded r-ideals in graded commutative rings with nonzero unity. Let G be a group, R be a G-graded commutative ring with nonzero unity and GI(R) be the set of all graded ideals of R. Suppose that ϕ: GI(R)→ GI(R)\bigcup\∅\ is a function. A proper graded ideal P of R is called a graded ϕ-r-ideal of R if whenever x, y are homogeneous elements of R such that xy∈ P-ϕ(P) and Ann(x) =\0\, then y∈ P. Several properties of graded ϕ-r-ideals have been examined.