On (uniformly) $S$-$w$-Noetherian rings and modules

TL;DR

This paper introduces and explores new classes of modules over rings, called ($u$-)$S$-$w$-Noetherian and ($u$-)$S$-$w$-principal ideal modules, providing characterizations and foundational properties.

Contribution

It defines and characterizes ($u$-)$S$-$w$-Noetherian modules and related concepts, expanding the theory of modules over rings.

Findings

Characterizations of ($u$-)$S$-$w$-Noetherian modules

Introduction of ($u$-)$S$-$w$-principal ideal modules

Foundational properties of the new module classes

Abstract

Let $R$ be a ring and $S$ a multiplicative subset of $R$. We introduce and study the notions of ($u$-)$S$-$w$-Noetherian modules and ($u$-)$S$-$w$-principal ideal modules. Some characterizations of these new concepts are given.