| Title:
|
On commutative twisted group rings (English) |
| Author:
|
Mollov, Todor Zh. |
| Author:
|
Nachev, Nako A. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
55 |
| Issue:
|
2 |
| Year:
|
2005 |
| Pages:
|
371-392 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $G$ be an abelian group, $R$ a commutative ring of prime characteristic $p$ with identity and $R_tG$ a commutative twisted group ring of $G$ over $R$. Suppose $p$ is a fixed prime, $G_p$ and $S(R_tG)$ are the $p$-components of $G$ and of the unit group $U(R_tG)$ of $R_tG$, respectively. Let $R^*$ be the multiplicative group of $R$ and let $f_\alpha (S)$ be the $ \alpha $-th Ulm-Kaplansky invariant of $S(R_tG)$ where $\alpha $ is any ordinal. In the paper the invariants $f_n(S)$, $ n\in \mathbb{N}\cup \lbrace 0\rbrace $, are calculated, provided $G_p=1$. Further, a commutative ring $R$ with identity of prime characteristic $p$ is said to be multiplicatively $p$-perfect if $(R^*)^p = R^*$. For these rings the invariants $f_\alpha (S)$ are calculated for any ordinal $\alpha $ and a description, up to an isomorphism, of the maximal divisible subgroup of $S(R_tG)$ is given. (English) |
| Keyword:
|
unit groups |
| Keyword:
|
isomorphism |
| Keyword:
|
Ulm-Kaplansky invariants |
| Keyword:
|
commutative twisted group rings |
| MSC:
|
13A10 |
| MSC:
|
16S34 |
| MSC:
|
16S35 |
| MSC:
|
16U60 |
| MSC:
|
20C07 |
| MSC:
|
20K10 |
| idZBL:
|
Zbl 1081.16033 |
| idMR:
|
MR2137144 |
| . |
| Date available:
|
2009-09-24T11:23:39Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127984 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
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|
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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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