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arXiv · 2602.18804

Locally prime modules

Sholastica Luambano·David Ssevviiri
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Abstract

For a commutative unital ring $R$ with fixed ideals $I$ and $J$, we introduce and study $I$-prime $R$-modules and $(I, J)$-prime $R$-modules together with their duals $I$-coprime $R$-modules and $(I,J)$-coprime $R$-modules respectively. We employ category-theoretic techniques to reveal their structural properties. Our main results are versions of the Greenlees-May Duality and the Matlis-Greenlees-May Equivalence to the setting of these prime and coprime modules. This generalizes work on $I$-reduced modules and $I$-coreduced modules. We demonstrate that these ``locally prime" modules serve as a tool for studying the classical ``globally prime" modules, creating a bridge between local and global primality.

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Sholastica Luambano, David Ssevviiri. 2026-02-21. Locally prime modules. https://arxiv.org/abs/2602.18804

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