Article
| Title: | On the invariance of certain types of generalized Cohen-Macaulay modules under Foxby equivalence (English) |
| Author: | Abolfath Beigi, Kosar |
| Author: | Divaani-Aazar, Kamran |
| Author: | Tousi, Massoud |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 72 |
| Issue: | 4 |
| Year: | 2022 |
| Pages: | 989-1002 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | Let $R$ be a local ring and $C$ a semidualizing module of $R$. We investigate the behavior of certain classes of generalized Cohen-Macaulay $R$-modules under the Foxby equivalence between the Auslander and Bass classes with respect to $C$. In particular, we show that generalized Cohen-Macaulay $R$-modules are invariant under this equivalence and if $M$ is a finitely generated $R$-module in the Auslander class with respect to $C$ such that $C\otimes _RM$ is surjective Buchsbaum, then $M$ is also surjective \hbox {Buchsbaum}.\looseness +1 (English) |
| Keyword: | Auslander class |
| Keyword: | Bass class |
| Keyword: | Buchsbaum module |
| Keyword: | dualizing module |
| Keyword: | generalized Cohen-Macaulay module |
| Keyword: | local cohomology |
| Keyword: | semidualizing module |
| Keyword: | surjective Buchsbaum module |
| MSC: | 13C14 |
| MSC: | 13D05 |
| MSC: | 13D45 |
| idZBL: | Zbl 07655776 |
| idMR: | MR4517589 |
| DOI: | 10.21136/CMJ.2022.0227-21 |
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| Date available: | 2022-11-28T11:33:55Z |
| Last updated: | 2023-04-11 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/151123 |
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