Generalised reduced modules

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.

13 pages

References in corpus (2)

• The locally nilradical for modules over commutative rings
• Nilpotent elements control the structure of a module