| Title:
|
A note on semilocal group rings (English) |
| Author:
|
Chin, Angelina Y. M. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
52 |
| Issue:
|
4 |
| Year:
|
2002 |
| Pages:
|
749-755 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $R$ be an associative ring with identity and let $J(R)$ denote the Jacobson radical of $R$. $R$ is said to be semilocal if $R/J(R)$ is Artinian. In this paper we give necessary and sufficient conditions for the group ring $RG$, where $G$ is an abelian group, to be semilocal. (English) |
| Keyword:
|
semilocal |
| Keyword:
|
group ring |
| MSC:
|
16L30 |
| MSC:
|
16S34 |
| MSC:
|
20C07 |
| idZBL:
|
Zbl 1014.16028 |
| idMR:
|
MR1940056 |
| . |
| Date available:
|
2009-09-24T10:56:20Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127761 |
| . |
| Reference:
|
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| Reference:
|
[2] I. G. Connell: On the group ring.Canad. J. Math. 15 (1963), 650–685. Zbl 0121.03502, MR 0153705, 10.4153/CJM-1963-067-0 |
| Reference:
|
[3] J. M. Goursaud: Sur les anneaux de groupes semi-parfaits.Canad. J. Math. 25 (1973), 922–928. Zbl 0269.16012, MR 0338054, 10.4153/CJM-1973-098-1 |
| Reference:
|
[4] K. Gulliksen, P. Ribenboim and T. M. Viswanathan: An elementary note on group rings.J. Reine Angew. Math. 242 (1970), 148–162. MR 0274609 |
| Reference:
|
[5] J. Lambek: Lectures on Rings and Modules.Blaisdell, Waltham, Mass., 1966. Zbl 0143.26403, MR 0206032 |
| Reference:
|
[6] J. Lawrence: Semilocal group rings and tensor products.Michigan Math. J. 22 (1975), 309–313. MR 0393107 |
| Reference:
|
[7] D. S. Passman: Advances in group rings.Israel J. Math. 19 (1974), 67–107. MR 0357477, 10.1007/BF02756627 |
| Reference:
|
[8] G. Renault: Sur les anneaux de groupes.C. R. Acad. Sci. Paris Ser. A 273 (1971), 84–87. Zbl 0275.16013, MR 0288189 |
| Reference:
|
[9] S. M. Woods: Some results on semi-perfect group rings.Canad. J. Math. 28 (1974), 121–129. Zbl 0242.16007, MR 0330212 |
| . |
