Direct decompositions and basic subgroups in commutative group rings

Peter Vassilev Danchev

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica (2006)

  • Volume: 45, Issue: 1, page 53-56
  • ISSN: 0231-9721

Abstract

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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).

How to cite

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Danchev, Peter Vassilev. "Direct decompositions and basic subgroups in commutative group rings." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 45.1 (2006): 53-56. <http://eudml.org/doc/32504>.

@article{Danchev2006,
abstract = {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).},
author = {Danchev, Peter Vassilev},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {direct decompositions; basic subgroups; normed units; group rings; direct decompositions; basic subgroups; normed units; group rings of Abelian groups; groups of normalized units},
language = {eng},
number = {1},
pages = {53-56},
publisher = {Palacký University Olomouc},
title = {Direct decompositions and basic subgroups in commutative group rings},
url = {http://eudml.org/doc/32504},
volume = {45},
year = {2006},
}

TY - JOUR
AU - Danchev, Peter Vassilev
TI - Direct decompositions and basic subgroups in commutative group rings
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 2006
PB - Palacký University Olomouc
VL - 45
IS - 1
SP - 53
EP - 56
AB - 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).
LA - eng
KW - direct decompositions; basic subgroups; normed units; group rings; direct decompositions; basic subgroups; normed units; group rings of Abelian groups; groups of normalized units
UR - http://eudml.org/doc/32504
ER -

References

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  1. Danchev P., Modular group algebras of coproducts of countable abelian groups, Hokkaido Math. J. 29, 2 (2000), 255–262. Zbl0967.20003MR1776708
  2. Danchev P., Sylow p -subgroups of abelian group rings, Serdica Math. J. 29, 1 (2003), 33–44. Zbl1035.16025MR1981103
  3. Danchev P., On a decomposition formula in commutative group rings, Miskolc Math. Notes 6, 2 (2005), 153–159. Zbl1110.16033MR2199160
  4. Danchev P., Basic subgroups in modular abelian group algebras, Czechoslovak Math. J. 56, 4 (2006). Zbl1167.16026MR2309958
  5. Fuchs L.: Infinite Abelian Groups. Volume I, Mir, Moskva, 1974, (in Russian). MR0346073
  6. Nachev N., Basic subgroups of the group of normalized units of modular group rings, Houston J. Math. 22, 2 (1996), 225–232. (1996) Zbl0859.16025MR1402745

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