| Title:
|
Finitistic dimension and restricted injective dimension (English) |
| Author:
|
Wu, Dejun |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
65 |
| Issue:
|
4 |
| Year:
|
2015 |
| Pages:
|
1023-1031 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We study the relations between finitistic dimensions and restricted injective dimensions. Let $R$ be a ring and $T$ a left $R$-module with $A=\mathop {\rm End}_RT$. If $_RT$ is selforthogonal, then we show that $\mathop {\rm rid}(T_A)\leq \mathop {\rm findim}(A_A)\leq \mathop {\rm findim}(_RT)+\mathop {\rm rid}(T_A)$. Moreover, if $R$ is a left noetherian ring and $T$ is a finitely generated left \mbox {$R$-module} with finite injective dimension, then $\mathop {\rm rid}(T_A)\leq \mathop {\rm findim}(A_A)\leq \mathop {\rm fin.inj.dim}(_RR)+\mathop {\rm rid}(T_A)$. Also we show by an example that the restricted injective dimensions of a module may be strictly smaller than the Gorenstein injective dimension. (English) |
| Keyword:
|
finitistic dimension |
| Keyword:
|
restricted injective dimension |
| Keyword:
|
tilting module |
| MSC:
|
18G10 |
| MSC:
|
18G20 |
| idZBL:
|
Zbl 06537708 |
| idMR:
|
MR3441333 |
| DOI:
|
10.1007/s10587-015-0225-y |
| . |
| Date available:
|
2016-01-13T09:16:02Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144790 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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