The locally nilradical for modules over commutative rings

Annet Kyomuhangi; David Ssevviiri

doi:10.1007/s13366-020-00491-x

paper

The locally nilradical for modules over commutative rings

arXiv:2003.02719 · doi:10.1007/s13366-020-00491-x

Abstract

Let $R$ be a commutative unital ring and $a \in R .$ We introduce and study properties of a functor $a Γ_{a} (-),$ called the locally nilradical on the category of $R$ -modules. $a Γ_{a} (-)$ is a generalisation of both the torsion functor (also called section functor) and Baer's lower nilradical for modules. Several local-global properties of the functor $a Γ_{a} (-)$ are established. As an application, results about reduced $R$ -modules are obtained and hitherto unknown ring theoretic radicals as well as structural theorems are deduced.

14 pages