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arXiv · 2306.12871

Applications of reduced and coreduced modules II: Radicality of the functor $\text{Hom}_R(R/I, -)$

David Ssevviiri
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Abstract

This is the second in a series of papers highlighting the applications of reduced and coreduced modules. Let $R$ be a commutative unital ring and $I$ be an ideal of $R$. We give necessary and sufficient conditions in terms of $I$-reduced $R$-modules for the functor $\text{Hom}_R(R/I, -)$ on an Abelian full subcategory of the category of $R$-modules to be a radical. $I$-reduced and $I$-coreduced $R$-modules provide a natural setting for a generalisation of Jans' correspondence, and lead to the construction of a new radical class of rings.

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David Ssevviiri. 2023-06-22. Applications of reduced and coreduced modules II: Radicality of the functor $\text{Hom}_R(R/I, -)$. https://arxiv.org/abs/2306.12871

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