| Title:
|
Relative Gorenstein injective covers with respect to a semidualizing module (English) |
| Author:
|
Tavasoli, Elham |
| Author:
|
Salimi, Maryam |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
67 |
| Issue:
|
1 |
| Year:
|
2017 |
| Pages:
|
87-95 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $R$ be a commutative Noetherian ring and let $C$ be a semidualizing $R$-module. We prove a result about the covering properties of the class of relative Gorenstein injective modules with respect to $C$ which is a generalization of Theorem 1 by Enochs and Iacob (2015). Specifically, we prove that if for every $G_{C}$-injective module $G$, the character module $G^{+}$ is $G_{C}$-flat, then the class $\mathcal {GI}_{C}(R)\cap \mathcal {A}_{C}(R)$ is closed under direct sums and direct limits. Also, it is proved that under the above hypotheses the class $\mathcal {GI}_{C}(R)\cap \mathcal {A}_{C}(R)$ is covering. (English) |
| Keyword:
|
semidualizing module |
| Keyword:
|
$G_{C}$-flat module |
| Keyword:
|
$G _{C}$-injective module |
| Keyword:
|
cover |
| Keyword:
|
envelope |
| MSC:
|
13D05 |
| MSC:
|
13D45 |
| MSC:
|
18G20 |
| idZBL:
|
Zbl 06738506 |
| idMR:
|
MR3633000 |
| DOI:
|
10.21136/CMJ.2017.0379-15 |
| . |
| Date available:
|
2017-03-13T12:06:08Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/146042 |
| . |
| Reference:
|
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