Applications of reduced and coreduced modules III: homological properties and coherence of functors
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arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866915202761490432 |
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| author | Ssevviiri, David |
| author_facet | Ssevviiri, David |
| contents | This is the third 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 show in different settings that $I$-reduced (resp. $I$-coreduced) $R$-modules facilitate the computation of local cohomology (resp. local homology) and provide conditions under which the $I$-torsion functor as well as the $I$-transform functor (resp. their duals) become coherent. We show that whenever every $R$-module is $I$-reduced (resp. $I$-coreduced), the cohomological dimension (resp. dual of the cohomological dimension) of an ideal $I$ of a ring $R$ coincides with the projective (resp. flat) dimension of the $R$-module $R/I$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_02937 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Applications of reduced and coreduced modules III: homological properties and coherence of functors Ssevviiri, David Commutative Algebra Rings and Algebras 13D45, 13D05, 13D07, 13C13 This is the third 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 show in different settings that $I$-reduced (resp. $I$-coreduced) $R$-modules facilitate the computation of local cohomology (resp. local homology) and provide conditions under which the $I$-torsion functor as well as the $I$-transform functor (resp. their duals) become coherent. We show that whenever every $R$-module is $I$-reduced (resp. $I$-coreduced), the cohomological dimension (resp. dual of the cohomological dimension) of an ideal $I$ of a ring $R$ coincides with the projective (resp. flat) dimension of the $R$-module $R/I$. |
| title | Applications of reduced and coreduced modules III: homological properties and coherence of functors |
| topic | Commutative Algebra Rings and Algebras 13D45, 13D05, 13D07, 13C13 |
| url | https://arxiv.org/abs/2502.02937 |