| 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 |
| . |
| Category:
|
math |
| . |
| 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 |
| . |
| Date available:
|
2022-11-28T11:33:55Z |
| Last updated:
|
2025-01-06 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/151123 |
| . |
| Reference:
|
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| Reference:
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