Locally prime modules
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866917286347014144 |
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| author | Luambano, Sholastica Ssevviiri, David |
| author_facet | Luambano, Sholastica Ssevviiri, David |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_18804 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Locally prime modules Luambano, Sholastica Ssevviiri, David Commutative Algebra Category Theory Rings and Algebras 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. |
| title | Locally prime modules |
| topic | Commutative Algebra Category Theory Rings and Algebras |
| url | https://arxiv.org/abs/2602.18804 |