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Trivial units for group rings over rings of algebraic integers


Authors: Allen Herman and Yuanlin Li
Journal: Proc. Amer. Math. Soc. 134 (2006), 631-635
MSC (2000): Primary 16S34; Secondary 16U60
DOI: https://doi.org/10.1090/S0002-9939-05-08018-4
Published electronically: July 18, 2005
MathSciNet review: 2180878
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Abstract: Let $G$ be a nontrivial torsion group and $R$ be the ring of integers of an algebraic number field. The necessary and sufficient conditions are given under which $RG$ has only trivial units.


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Additional Information

Allen Herman
Affiliation: Department of Mathematics and Statistics, University of Regina, Regina, Saskatchewan, Canada S4S 0A2
Email: aherman@math.uregina.ca

Yuanlin Li
Affiliation: Department of Mathematics, Brock University, St. Catharine’s, Ontario, Canada L2S 3A1
Email: yli@brocku.ca

DOI: https://doi.org/10.1090/S0002-9939-05-08018-4
Keywords: Group rings, units, rings of algebraic integers
Received by editor(s): August 6, 2004
Received by editor(s) in revised form: October 1, 2004
Published electronically: July 18, 2005
Additional Notes: This research was supported in part by Discovery Grants from the Natural Sciences and Engineering Research Council of Canada.
Communicated by: Martin Lorenz
Article copyright: © Copyright 2005 American Mathematical Society

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