| Title:
|
Estimates of global dimension (English) |
| Author:
|
Jiaqun, Wei |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
56 |
| Issue:
|
2 |
| Year:
|
2006 |
| Pages:
|
773-780 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this note we show that for a $\ast ^{n}$-module, in particular, an almost $n$-tilting module, $P$ over a ring $R$ with $A=\mathop {\mathrm End}_{R}P$ such that $P_A$ has finite flat dimension, the upper bound of the global dimension of $A$ can be estimated by the global dimension of $R$ and hence generalize the corresponding results in tilting theory and the ones in the theory of $\ast $-modules. As an application, we show that for a finitely generated projective module over a VN regular ring $R$, the global dimension of its endomorphism ring is not more than the global dimension of $R$. (English) |
| Keyword:
|
global dimension |
| Keyword:
|
$\ast $-module |
| MSC:
|
16D90 |
| MSC:
|
16E10 |
| MSC:
|
16E30 |
| idZBL:
|
Zbl 1157.16301 |
| idMR:
|
MR2291774 |
| . |
| Date available:
|
2009-09-24T11:37:57Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128104 |
| . |
| Reference:
|
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| . |
