On j-Artinian Modules Over Commutative Rings

TL;DR

This paper extends the concept of j-Artinian rings to modules over commutative rings, providing characterizations, an analogue of Akizuki's theorem, and exploring extensions to amalgamated structures.

Contribution

It introduces the notion of j-Artinian modules, characterizes them, and establishes an analogue of Akizuki's theorem, expanding the theory from rings to modules.

Findings

Characterization of j-Artinian modules

An analogue of Akizuki's theorem for j-Artinian modules

Discussion on extension to amalgamated structures

Abstract

Researchers introduced the notion of j-Artinian rings in [3] and obtained significant results concerning this new class of rings. Motivated by their definition and findings, we extend the study to modules by introducing the concept of j-Artinian modules. Recall from [9] that, if R is a commutative ring with identity, M is an R-module, and j is a submodule of M, then a submodule N of M is called a j-submodule if N \not\subseteq j. We say that M is a j-Artinian R-module if every descending chain of j-submodules becomes stationary. In this paper, we provide a characterization of j-Artinian modules. Moreover, we establish an analogue of Akizuki's theorem in this context and discuss its extension to amalgamated structures.