Generalised reduced modules

TL;DR

This paper introduces and studies generalized notions of reduced modules over commutative rings, extending classical concepts and deriving new properties for these modules and related rings.

Contribution

It defines $a^{t}$-reduced and universally $a^{t}$-reduced modules, generalizing existing reduced modules, and explores their properties and implications for reduced rings.

Findings

Retrieved known results for reduced modules when t=1

Obtained new properties of $a^{t}$-reduced modules

Deduced results about reduced rings from module properties

Abstract

Let $R$ be a commutative unital ring, $a\in R$ and $t$ a positive integer. $a^{t}$-reduced $R$-modules and universally $a^{t}$-reduced $R$-modules are defined and their properties given. Known (resp. new) results about reduced $R$-modules are retrieved (resp. obtained) by taking $t=1$ and results about reduced rings are deduced.