Modules (co)reduced relative to another module
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866910404987322368 |
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| author | Abebaw, Tilahun Mamo, Amanuel Ssevviiri, David Teshome, Zelalem |
| author_facet | Abebaw, Tilahun Mamo, Amanuel Ssevviiri, David Teshome, Zelalem |
| contents | Let $R$ be a commutative unital ring, $\mathfrak{ a}$ an ideal of $R$ and $M$ a fixed $R$-module. We introduce and study generalisations of $\mathfrak{a}$-reduced modules, $\mathfrak{R}_{\mathfrak{ a}}$ and $\mathfrak{a}$-coreduced modules, $\mathfrak{C}_{\mathfrak{ a}}$ studied in the literature. They are called modules $\mathfrak{ a}$-reduced with respect to $M$, $\mathfrak{R}^{M}_{\mathfrak{ a}}$ and modules $\mathfrak{ a}$-coreduced with respect to $M$, $\mathfrak{C}^{M}_{\mathfrak{ a}}$. The paper lifts several known results about $\mathfrak{R}_{\mathfrak{ a}}$ and $\mathfrak{C}_{\mathfrak{ a}}$ to larger classes of modules $\mathfrak{R}^{M}_{\mathfrak{ a}}$ and $\mathfrak{C}^{M}_{\mathfrak{ a}}$ respectively. Results about $\mathfrak{R}_{\mathfrak{ a}}$ and $\mathfrak{C}_{\mathfrak{ a}}$ can be retrieved by taking $M= R$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_06874 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Modules (co)reduced relative to another module Abebaw, Tilahun Mamo, Amanuel Ssevviiri, David Teshome, Zelalem Commutative Algebra Category Theory Rings and Algebras Representation Theory 13C13, 13D07, 13D45, 18A35 Let $R$ be a commutative unital ring, $\mathfrak{ a}$ an ideal of $R$ and $M$ a fixed $R$-module. We introduce and study generalisations of $\mathfrak{a}$-reduced modules, $\mathfrak{R}_{\mathfrak{ a}}$ and $\mathfrak{a}$-coreduced modules, $\mathfrak{C}_{\mathfrak{ a}}$ studied in the literature. They are called modules $\mathfrak{ a}$-reduced with respect to $M$, $\mathfrak{R}^{M}_{\mathfrak{ a}}$ and modules $\mathfrak{ a}$-coreduced with respect to $M$, $\mathfrak{C}^{M}_{\mathfrak{ a}}$. The paper lifts several known results about $\mathfrak{R}_{\mathfrak{ a}}$ and $\mathfrak{C}_{\mathfrak{ a}}$ to larger classes of modules $\mathfrak{R}^{M}_{\mathfrak{ a}}$ and $\mathfrak{C}^{M}_{\mathfrak{ a}}$ respectively. Results about $\mathfrak{R}_{\mathfrak{ a}}$ and $\mathfrak{C}_{\mathfrak{ a}}$ can be retrieved by taking $M= R$. |
| title | Modules (co)reduced relative to another module |
| topic | Commutative Algebra Category Theory Rings and Algebras Representation Theory 13C13, 13D07, 13D45, 18A35 |
| url | https://arxiv.org/abs/2404.06874 |