Centers of Endomorphism Rings and Reflexivity
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908574231298048 |
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| author | Dey, Souvik Lyle, Justin |
| author_facet | Dey, Souvik Lyle, Justin |
| contents | Let $R$ be a local ring and let $M$ be a finitely generated $R$-module. Appealing to the natural left module structure of $M$ over its endomorphism ring and corresponding center $Z(\operatorname{End}_R(M))$, we study when various homological properties of $M$ are sufficient to force $M$ to have a nonzero free summand. Consequences of our work include a partial converse to a well-known result of Lindo describing $Z(\operatorname{End}_R(M))$ when $M$ is faithful and reflexive, as well as some applications to the famous Huneke-Wiegand conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_02210 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Centers of Endomorphism Rings and Reflexivity Dey, Souvik Lyle, Justin Commutative Algebra Rings and Algebras 13D07, 16S50, 13C14 Let $R$ be a local ring and let $M$ be a finitely generated $R$-module. Appealing to the natural left module structure of $M$ over its endomorphism ring and corresponding center $Z(\operatorname{End}_R(M))$, we study when various homological properties of $M$ are sufficient to force $M$ to have a nonzero free summand. Consequences of our work include a partial converse to a well-known result of Lindo describing $Z(\operatorname{End}_R(M))$ when $M$ is faithful and reflexive, as well as some applications to the famous Huneke-Wiegand conjecture. |
| title | Centers of Endomorphism Rings and Reflexivity |
| topic | Commutative Algebra Rings and Algebras 13D07, 16S50, 13C14 |
| url | https://arxiv.org/abs/2510.02210 |