Applications of reduced and coreduced modules II: Radicality of the functor $\text{Hom}_R(R/I, -)$
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866912447793725440 |
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| author | Ssevviiri, David |
| author_facet | Ssevviiri, David |
| contents | 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 and $I$-coreduced $R$-modules for the functor $\text{Hom}_R(R/I, -)$ on the abelian full subcategory of the category of $R$-modules to be a radical. These conditions further provide a setting for the generalisation of Jans' correspondence, and lead to a new radical class of rings. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2306_12871 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Applications of reduced and coreduced modules II: Radicality of the functor $\text{Hom}_R(R/I, -)$ Ssevviiri, David Commutative Algebra Rings and Algebras 16S90, 13D30, 16D80, 13D07 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 and $I$-coreduced $R$-modules for the functor $\text{Hom}_R(R/I, -)$ on the abelian full subcategory of the category of $R$-modules to be a radical. These conditions further provide a setting for the generalisation of Jans' correspondence, and lead to a new radical class of rings. |
| title | Applications of reduced and coreduced modules II: Radicality of the functor $\text{Hom}_R(R/I, -)$ |
| topic | Commutative Algebra Rings and Algebras 16S90, 13D30, 16D80, 13D07 |
| url | https://arxiv.org/abs/2306.12871 |