| Title:
|
A note on group algebras of $p$-primary abelian groups (English) |
| Author:
|
Ullery, William |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
36 |
| Issue:
|
1 |
| Year:
|
1995 |
| Pages:
|
11-14 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Suppose $p$ is a prime number and $R$ is a commutative ring with unity of characteristic 0 in which $p$ is not a unit. Assume that $G$ and $H$ are $p$-primary abelian groups such that the respective group algebras $RG$ and $RH$ are $R$-isomorphic. Under certain restrictions on the ideal structure of $R$, it is shown that $G$ and $H$ are isomorphic. (English) |
| Keyword:
|
commutative group algebras |
| Keyword:
|
isomorphism |
| MSC:
|
16S34 |
| MSC:
|
20C07 |
| MSC:
|
20K10 |
| idZBL:
|
Zbl 0828.20005 |
| idMR:
|
MR1334408 |
| . |
| Date available:
|
2009-01-08T18:15:35Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118726 |
| . |
| Reference:
|
[K] Karpilovsky G.: Commutative Group Algebras.Marcel Dekker New York (1983). Zbl 0508.16010, MR 0704185 |
| Reference:
|
[M] May W.: Isomorphism of group algebras.J. Algebra 40 (1976), 10-18. Zbl 0329.20002, MR 0414618 |
| Reference:
|
[U] Ullery W.: On isomorphism of group algebras of torsion abelian groups.Rocky Mtn. J. Math. 22 (1992), 1111-1122. Zbl 0773.16008, MR 1183707 |
| . |
