Almost graded multiplication and almost graded comultiplication modules

[摘要] Let G be a group with identity e , R be a G -graded commutative ring with a nonzero unity 1 and M be a G -graded R -module. In this article, we introduce and study the concept of almost graded multiplication modules as a generalization of graded multiplication modules; a graded R -module M is said to be almost graded multiplication if whenever a∈h(R)a\in h(R) satisfies AnnR(aM)=AnnR(M){\text{Ann}}_{R}(aM)={\text{Ann}}_{R}(M), then (0:Ma)={0}(0{:}_{M}a)=\{0\}. Also, we introduce and study the concept of almost graded comultiplication modules as a generalization of graded comultiplication modules; a graded R -module M is said to be almost graded comultiplication if whenever a∈h(R)a\in h(R) satisfies AnnR(aM)=AnnR(M){\text{Ann}}_{R}(aM)={\text{Ann}}_{R}(M), then aM=MaM=M. We investigate several properties of these classes of graded modules.

[学科分类] 外科医学

[关键词] graded multiplication module;graded comultiplication module