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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:
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


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