| Title:
|
On the regularity of group algebras (English) |
| Author:
|
Bovdi, A. A. |
| Author:
|
Lángi, T. P. |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
32 |
| Issue:
|
2 |
| Year:
|
1996 |
| Pages:
|
117-121 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We describe $n$-regular and $n$-weakly regular group algebras. $KG$ is $n$-regular if and only if one of the following conditions holds: \item{(1)} $char K=0$ and $G$ is locally finite; or \item{(2)} $char K=p$, $\,G$ is locally finite, $\,\Delta^p(G)$ is finite and contains all the elements of $G$ of $p$-power order and $\,rad(K\Delta^p(G))^n=0$. (English) |
| Keyword:
|
group algebra |
| Keyword:
|
n-weakly regular ring |
| Keyword:
|
n-regular ring |
| MSC:
|
16E50 |
| MSC:
|
16S34 |
| MSC:
|
20C07 |
| idZBL:
|
Zbl 0906.16012 |
| idMR:
|
MR1407343 |
| . |
| Date available:
|
2008-06-06T21:30:29Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107566 |
| . |
| Reference:
|
[1] Anderson, D., D.: Generalizations of Boolean rings. Boolean rings and von Neumann regular rings.Comment. Math. Univ. St. Pauli 35 (1986), 69-76. MR 0838191 |
| Reference:
|
[2] Auslander, M.: On regular group rings.Proc. Amer. Math. Soc. 8 (1957), 658-664. Zbl 0079.26703, MR 0087670 |
| Reference:
|
[3] Connel, I.: On the group ring.Can. J. Math. 15 (1963), 650-685. MR 0153705 |
| Reference:
|
[4] Gupta, V.: A generalization of strongly regular rings.Acta Math. Hung. 43 (1984), No 1-2, 57-61. Zbl 0535.16015, MR 0731964 |
| Reference:
|
[5] Passman, D. S.: Algebraic structure of group rings.Interscience, New-York, 1977. Zbl 0368.16003, MR 0470211 |
| Reference:
|
[6] Vasantha Kandasamy, W. B.: s-weakly regular group rings.Archiv. Math. (Brno) 29 (1993), No 1-2, 39-41. Zbl 0812.16003, MR 1242627 |
| Reference:
|
[7] Villamayor, O. E.: On weak dimenson of algebras.Pacif. J. Math. 9 (1959), 491-502. MR 0108527 |
| Reference:
|
[8] Sehgal, S. K.: Topics in group rings.Marcel Dekker,Inc., New-York and Basel, 1978. Zbl 0411.16004, MR 0508515 |
| . |
