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

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.