| Title:
|
$(n,d)$-injective covers, $n$-coherent rings, and $(n,d)$-rings (English) |
| Author:
|
Li, Weiqing |
| Author:
|
Ouyang, Baiyu |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
64 |
| Issue:
|
2 |
| Year:
|
2014 |
| Pages:
|
289-304 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
It is known that a ring $R$ is left Noetherian if and only if every left $R$-module has an injective (pre)cover. We show that $(1)$ if $R$ is a right $n$-coherent ring, then every right $R$-module has an $(n,d)$-injective (pre)cover; $(2)$ if $R$ is a ring such that every $(n,0)$-injective right $R$-module is $n$-pure extending, and if every right $R$-module has an $(n,0)$-injective cover, then $R$ is right $n$-coherent. As applications of these results, we give some characterizations of $(n,d)$-rings, von Neumann regular rings and semisimple rings. (English) |
| Keyword:
|
cover |
| Keyword:
|
envelope |
| Keyword:
|
$n$-coherent ring |
| Keyword:
|
$(n,d)$-injective |
| Keyword:
|
$(n,d)$-ring |
| MSC:
|
16D40 |
| MSC:
|
16D50 |
| MSC:
|
16E40 |
| MSC:
|
16P70 |
| MSC:
|
18G25 |
| idZBL:
|
Zbl 06391494 |
| idMR:
|
MR3277736 |
| DOI:
|
10.1007/s10587-014-0101-1 |
| . |
| Date available:
|
2014-11-10T09:26:25Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143997 |
| . |
| Reference:
|
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