Ascent and descent of Artinian module structures under flat base changes
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913959707148288 |
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| author | Chau, Tran Do Minh Nhan, Le Thanh |
| author_facet | Chau, Tran Do Minh Nhan, Le Thanh |
| contents | Let $φ: R\rightarrow S$ be a flat local homomorphism between commutative Noetherian local rings. In this paper, the ascent and descent of Artinian module structures between $R$ and $S$ are investigated. For an Artinian $R$-module $A$, the structure of $A\otimes_RS$ is described. As an application, the Artinianess of certain local cohomology modules is clarified. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_19019 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Ascent and descent of Artinian module structures under flat base changes Chau, Tran Do Minh Nhan, Le Thanh Commutative Algebra N 13B40, 13E10, 13E05, 13D45 13B40, 13E10, 13E05, 13D45 Let $φ: R\rightarrow S$ be a flat local homomorphism between commutative Noetherian local rings. In this paper, the ascent and descent of Artinian module structures between $R$ and $S$ are investigated. For an Artinian $R$-module $A$, the structure of $A\otimes_RS$ is described. As an application, the Artinianess of certain local cohomology modules is clarified. |
| title | Ascent and descent of Artinian module structures under flat base changes |
| topic | Commutative Algebra N 13B40, 13E10, 13E05, 13D45 13B40, 13E10, 13E05, 13D45 |
| url | https://arxiv.org/abs/2507.19019 |