| Title:
|
Totally reflexive modules with respect to a semidualizing bimodule (English) |
| Author:
|
Zhang, Zhen |
| Author:
|
Zhu, Xiaosheng |
| Author:
|
Yan, Xiaoguang |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
63 |
| Issue:
|
2 |
| Year:
|
2013 |
| Pages:
|
385-402 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $S$ and $R$ be two associative rings, let $ _{S}C_{R}$ be a semidualizing $(S,R)$-bimodule. We introduce and investigate properties of the totally reflexive module with respect to $_{S}C_{R}$ and we give a characterization of the class of the totally $C_{R}$-reflexive modules over any ring $R$. Moreover, we show that the totally $C_{R}$-reflexive module with finite projective dimension is exactly the finitely generated projective right $R$-module. We then study the relations between the class of totally reflexive modules and the Bass class with respect to a semidualizing bimodule. The paper contains several results which are new in the commutative Noetherian setting. (English) |
| Keyword:
|
semidualizing bimodule |
| Keyword:
|
totally reflexive module |
| Keyword:
|
Bass class |
| Keyword:
|
precover |
| Keyword:
|
preenvelope |
| MSC:
|
16D20 |
| MSC:
|
16D40 |
| MSC:
|
16E05 |
| MSC:
|
16E10 |
| MSC:
|
16E30 |
| idZBL:
|
Zbl 06236418 |
| idMR:
|
MR3073965 |
| DOI:
|
10.1007/s10587-013-0024-2 |
| . |
| Date available:
|
2013-07-18T14:54:13Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143319 |
| . |
| Reference:
|
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