nil-$M$-Noetherian and nil-$M$-Artinian modules

TL;DR

This paper introduces and studies nil-M-Noetherian and nil-M-Artinian modules, generalizing classical Noetherian and Artinian modules, along with related nil-versions of algebraic concepts.

Contribution

It proposes new nil-based generalizations of Noetherian and Artinian modules and explores their properties and related algebraic concepts.

Findings

Defined nil-M-Noetherian and nil-M-Artinian modules

Established basic properties and relationships of these modules

Introduced nil versions of classical algebraic concepts

Abstract

Let R be a commutative ring with identity and M be an R- module. The aim of this paper is to introduce and investigate the notions of nil-M-Noetherian and nil-M-Artinian modules as generalizations of Noetherian and Artinian modules. Also, in this regard we introduce nil versions of some algebraic concepts.