Endomorphism algebras over commutative rings and torsion in self tensor products
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866910963425345536 |
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| author | Lyle, Justin |
| author_facet | Lyle, Justin |
| contents | Let $R$ be a commutative Noetherian local ring. We study tensor products involving a finitely generated $R$-module $M$ through the natural action of its endomorphism ring. In particular, we study torsion properties of self tensor products in the case where $\operatorname{End}_R(M)$ has an $R^*$-algebra structure, and prove that if $M$ is indecomposable, then $M \otimes_{\operatorname{End}_R(M)} M$ must always have torsion in this case under mild hypotheses. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_14134 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Endomorphism algebras over commutative rings and torsion in self tensor products Lyle, Justin Commutative Algebra Rings and Algebras 13C12, 13H99, 16S50 Let $R$ be a commutative Noetherian local ring. We study tensor products involving a finitely generated $R$-module $M$ through the natural action of its endomorphism ring. In particular, we study torsion properties of self tensor products in the case where $\operatorname{End}_R(M)$ has an $R^*$-algebra structure, and prove that if $M$ is indecomposable, then $M \otimes_{\operatorname{End}_R(M)} M$ must always have torsion in this case under mild hypotheses. |
| title | Endomorphism algebras over commutative rings and torsion in self tensor products |
| topic | Commutative Algebra Rings and Algebras 13C12, 13H99, 16S50 |
| url | https://arxiv.org/abs/2310.14134 |