| Title:
|
A family of noetherian rings with their finite length modules under control (English) |
| Author:
|
Schmidmeier, Markus |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
52 |
| Issue:
|
3 |
| Year:
|
2002 |
| Pages:
|
545-552 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We investigate the category $\text{mod}\Lambda $ of finite length modules over the ring $\Lambda =A\otimes _k\Sigma $, where $\Sigma $ is a V-ring, i.e. a ring for which every simple module is injective, $k$ a subfield of its centre and $A$ an elementary $k$-algebra. Each simple module $E_j$ gives rise to a quasiprogenerator $P_j=A\otimes E_j$. By a result of K. Fuller, $P_j$ induces a category equivalence from which we deduce that $\text{mod}\Lambda \simeq \coprod _jbad hbox P_j$. As a consequence we can (1) construct for each elementary $k$-algebra $A$ over a finite field $k$ a nonartinian noetherian ring $\Lambda $ such that $\text{mod}A\simeq \text{mod}\Lambda $, (2) find twisted versions $\Lambda $ of algebras of wild representation type such that $\Lambda $ itself is of finite or tame representation type (in mod), (3) describe for certain rings $\Lambda $ the minimal almost split morphisms in $\text{mod} \Lambda $ and observe that almost all of these maps are not almost split in $\text{Mod}\Lambda $. (English) |
| Keyword:
|
V-ring |
| Keyword:
|
progenerator |
| Keyword:
|
almost split morphisms |
| MSC:
|
16D50 |
| MSC:
|
16D60 |
| MSC:
|
16D90 |
| MSC:
|
16G10 |
| MSC:
|
16G20 |
| MSC:
|
16G60 |
| MSC:
|
16G70 |
| MSC:
|
16P40 |
| idZBL:
|
Zbl 1014.16014 |
| idMR:
|
MR1923260 |
| . |
| Date available:
|
2009-09-24T10:54:00Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127742 |
| . |
| 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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| 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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| . |
