| Title:
|
Direct decompositions and basic subgroups in commutative group rings (English) |
| Author:
|
Danchev, P. V. |
| Language:
|
English |
| Journal:
|
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica |
| ISSN:
|
0231-9721 |
| Volume:
|
45 |
| Issue:
|
1 |
| Year:
|
2006 |
| Pages:
|
53-56 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
An attractive interplay between the direct decompositions and the explicit form of basic subgroups in group rings of abelian groups over a commutative unitary ring are established. In particular, as a consequence, we give a simpler confirmation of a more general version of our recent result in this aspect published in Czechoslovak Math. J. (2006). (English) |
| Keyword:
|
direct decompositions |
| Keyword:
|
basic subgroups |
| Keyword:
|
normed units |
| Keyword:
|
group rings |
| MSC:
|
16S34 |
| MSC:
|
16U60 |
| MSC:
|
20C07 |
| MSC:
|
20K10 |
| MSC:
|
20K21 |
| MSC:
|
20K27 |
| idZBL:
|
Zbl 1122.16308 |
| idMR:
|
MR2321297 |
| . |
| Date available:
|
2009-08-21T07:04:18Z |
| Last updated:
|
2012-05-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/133441 |
| . |
| Reference:
|
[1] Danchev P.: Modular group algebras of coproducts of countable abelian groups.Hokkaido Math. J. 29, 2 (2000), 255–262. Zbl 0967.20003, MR 1776708 |
| Reference:
|
[2] Danchev P.: Sylow $p$-subgroups of abelian group rings.Serdica Math. J. 29, 1 (2003), 33–44. Zbl 1035.16025, MR 1981103 |
| Reference:
|
[3] Danchev P.: On a decomposition formula in commutative group rings.Miskolc Math. Notes 6, 2 (2005), 153–159. Zbl 1110.16033, MR 2199160 |
| Reference:
|
[4] Danchev P.: Basic subgroups in modular abelian group algebras.Czechoslovak Math. J. 56, 4 (2006). Zbl 1167.16026, MR 2309958 |
| Reference:
|
[5] Fuchs L.: Infinite Abelian Groups. Volume I: Mir, Moskva.1974, (in Russian). MR 0346073 |
| Reference:
|
[6] Nachev N.: Basic subgroups of the group of normalized units of modular group rings.Houston J. Math. 22, 2 (1996), 225–232. Zbl 0859.16025, MR 1402745 |
| . |
