| Title:
|
Some results on $(n,d)$-injective modules, $(n,d)$-flat modules and $n$-coherent rings (English) |
| Author:
|
Zhu, Zhanmin |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
56 |
| Issue:
|
4 |
| Year:
|
2015 |
| Pages:
|
505-513 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $n,d$ be two non-negative integers. A left $R$-module $M$ is called $(n,d)$-injective, if ${\rm Ext}^{d+1}(N, M)=0$ for every $n$-presented left $R$-module $N$. A right $R$-module $V$ is called $(n,d)$-flat, if ${\rm Tor}_{d+1}(V, N)=0$ for every $n$-presented left $R$-module $N$. A left $R$-module $M$ is called weakly $n$-$FP$-injective, if ${\rm Ext}^n(N, M)=0$ for every $(n+1)$-presented left $R$-module $N$. A right $R$-module $V$ is called weakly $n$-flat, if ${\rm Tor}_n(V, N)=0$ for every $(n+1)$-presented left $R$-module $N$. In this paper, we give some characterizations and properties of $(n,d)$-injective modules and $(n,d)$-flat modules in the cases of $n\geq d+1$ or $n> d+1$. Using the concepts of weakly $n$-$FP$-injectivity and weakly $n$-flatness of modules, we give some new characterizations of left $n$-coherent rings. (English) |
| Keyword:
|
$(n,d)$-injective modules |
| Keyword:
|
$(n,d)$-flat modules |
| Keyword:
|
$n$-coherent rings |
| MSC:
|
16D40 |
| MSC:
|
16D50 |
| MSC:
|
16P70 |
| idZBL:
|
Zbl 06537720 |
| idMR:
|
MR3434225 |
| DOI:
|
10.14712/1213-7243.2015.133 |
| . |
| Date available:
|
2015-12-17T11:49:33Z |
| Last updated:
|
2018-01-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144755 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| . |
