Tor algebra of local rings with decomposable maximal ideal
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866914096516956160 |
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| author | Nasseh, Saeed Ono, Maiko Yoshino, Yuji |
| author_facet | Nasseh, Saeed Ono, Maiko Yoshino, Yuji |
| contents | Let $(R,{\frak{m}}_R)$ be a commutative noetherian local ring. Assuming that ${\frak{m}}_R=$$I\oplus J$ is a direct sum decomposition, where $I$ and $J$ are non-zero ideals of $R$, we describe the structure of the Tor algebra of $R$ in terms of the Tor algebras of the rings $R/I$ and $R/J$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_01784 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Tor algebra of local rings with decomposable maximal ideal Nasseh, Saeed Ono, Maiko Yoshino, Yuji Commutative Algebra 13D07, 16E30, 16E45 Let $(R,{\frak{m}}_R)$ be a commutative noetherian local ring. Assuming that ${\frak{m}}_R=$$I\oplus J$ is a direct sum decomposition, where $I$ and $J$ are non-zero ideals of $R$, we describe the structure of the Tor algebra of $R$ in terms of the Tor algebras of the rings $R/I$ and $R/J$. |
| title | Tor algebra of local rings with decomposable maximal ideal |
| topic | Commutative Algebra 13D07, 16E30, 16E45 |
| url | https://arxiv.org/abs/2507.01784 |