Graded S-Noetherian Modules

Authors : Ajim Uddin ANSARI, B K SHARMA

Pages : 87-108

Doi:10.24330/ieja.1229782

View : 19 | Download : 11

Publication Date : 2023-01-09

Article Type : Research Paper

Abstract :Let $G$ be an abelian group and $S$ a given multiplicatively closed subset of a commutative $G$-graded ring $A$ consisting of homogeneous elements. In this paper, we introduce and study $G$-graded $S$-Noetherian modules which are a generalization of $S$-Noetherian modules. We characterize $G$-graded $S$-Noetherian modules in terms of $S$-Noetherian modules. For instance, a $G$-graded $A$-module $M$ is $G$-graded $S$-Noetherian if and only if $M$ is $S$-Noetherian, provided $G$ is finitely generated and $S$ is countable. Also, we generalize some results on $G$-graded Noetherian rings and modules to $G$-graded $S$-Noetherian rings and modules.
Keywords : Noetherian module, graded Noetherian module, S Noetherian module, graded S Noetherian module, graded strong S Noetherian module