2020/08/13 by Tariq Alraqad, Alraqad, Tariq, Hicham Saber +3
Mathematics · #Advanced Topics in Algebra #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Rings and Algebras (math.RA) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2008.06090
openalex publication_date 2020/08/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let G be a group with identity e and R a commutative G-graded ring with a nonzero unity 1. In this article, we introduce the concepts of graded r-submodules and graded special r-submodules, which are generalizations for the notion of graded r-ideals. For a nonzero G-graded R-module M, a proper graded R-submodule K of M is said to be graded r-submodule (resp., graded special r-submodule) if whenever a∈ h(R) and x∈ h(M) such that ax∈ K with AnnM(a)=\0\ (resp., AnnR(x)=\0\), then x∈ K (resp., a∈ (K:RM)). We study various properties of graded r-submodules and graded special r-submodules, and we give several illustration examples of these two new classes of graded modules.