G -nilpotent units of commutative group rings

Peter Vassilev Danchev

Commentationes Mathematicae Universitatis Carolinae (2012)

  • Volume: 53, Issue: 2, page 179-187
  • ISSN: 0010-2628

Abstract

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Suppose R is a commutative unital ring and G is an abelian group. We give a general criterion only in terms of R and G when all normalized units in the commutative group ring R G are G -nilpotent. This extends recent results published in [Extracta Math., 2008–2009] and [Ann. Sci. Math. Québec, 2009].

How to cite

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Danchev, Peter Vassilev. "$G$-nilpotent units of commutative group rings." Commentationes Mathematicae Universitatis Carolinae 53.2 (2012): 179-187. <http://eudml.org/doc/246916>.

@article{Danchev2012,
abstract = {Suppose $R$ is a commutative unital ring and $G$ is an abelian group. We give a general criterion only in terms of $R$ and $G$ when all normalized units in the commutative group ring $RG$ are $G$-nilpotent. This extends recent results published in [Extracta Math., 2008–2009] and [Ann. Sci. Math. Québec, 2009].},
author = {Danchev, Peter Vassilev},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {group rings; normalized units; nilpotents; idempotents; decompositions; abelian groups; commutative group rings; normalized units; nilpotent units; idempotents; decompositions; Abelian groups},
language = {eng},
number = {2},
pages = {179-187},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {$G$-nilpotent units of commutative group rings},
url = {http://eudml.org/doc/246916},
volume = {53},
year = {2012},
}

TY - JOUR
AU - Danchev, Peter Vassilev
TI - $G$-nilpotent units of commutative group rings
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2012
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 53
IS - 2
SP - 179
EP - 187
AB - Suppose $R$ is a commutative unital ring and $G$ is an abelian group. We give a general criterion only in terms of $R$ and $G$ when all normalized units in the commutative group ring $RG$ are $G$-nilpotent. This extends recent results published in [Extracta Math., 2008–2009] and [Ann. Sci. Math. Québec, 2009].
LA - eng
KW - group rings; normalized units; nilpotents; idempotents; decompositions; abelian groups; commutative group rings; normalized units; nilpotent units; idempotents; decompositions; Abelian groups
UR - http://eudml.org/doc/246916
ER -

References

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