| Title:
|
$k$-torsionless modules with finite Gorenstein dimension (English) |
| Author:
|
Salimi, Maryam |
| Author:
|
Tavasoli, Elham |
| Author:
|
Yassemi, Siamak |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
62 |
| Issue:
|
3 |
| Year:
|
2012 |
| Pages:
|
663-672 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $R$ be a commutative Noetherian ring. It is shown that the finitely generated $R$-module $M$ with finite Gorenstein dimension is reflexive if and only if $M_{\mathfrak p}$ is reflexive for ${\mathfrak p} \in {\rm Spec}(R) $ with ${\rm depth}(R_{\mathfrak p}) \leq 1$, and ${\mbox {G-{\rm dim}}}_{R_{\mathfrak p}} (M_{\mathfrak p}) \leq {\rm depth}(R_{\mathfrak p})-2 $ for ${\mathfrak p}\in {\rm Spec} (R) $ with ${\rm depth}(R_{\mathfrak p})\geq 2 $. This gives a generalization of Serre and Samuel's results on reflexive modules over a regular local ring and a generalization of a recent result due to Belshoff. In addition, for $n\geq 2$ we give a characterization of $n$-Gorenstein rings via Gorenstein dimension of the dual of modules. Finally it is shown that every $R$-module has a $k$-torsionless cover provided $R$ is a $k$-Gorenstein ring. (English) |
| Keyword:
|
torsionless module |
| Keyword:
|
reflexive module |
| Keyword:
|
Gorenstein dimension |
| MSC:
|
13C13 |
| MSC:
|
13C15 |
| MSC:
|
13D05 |
| idZBL:
|
Zbl 1265.13013 |
| idMR:
|
MR2984627 |
| DOI:
|
10.1007/s10587-012-0058-x |
| . |
| Date available:
|
2012-11-10T21:05:45Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143018 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| . |
