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arXiv · 2003.02719

The locally nilradical for modules over commutative rings

Annet Kyomuhangi·David Ssevviiri
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Abstract

Let $R$ be a commutative unital ring and $a\in R.$ We introduce and study properties of a functor $aΓ_{a}(-),$ called the locally nilradical on the category of $R$-modules. $aΓ_{a}(-)$ 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 $aΓ_{a}(-)$ 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.

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Annet Kyomuhangi, David Ssevviiri. 2020-03-05. The locally nilradical for modules over commutative rings. https://doi.org/10.1007/s13366-020-00491-x

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