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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
Published electronically: July 18, 2005
MathSciNet review: 2180878
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Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

  • 1. A. Herman, Y. Li and M.M. Parmenter, Trivial units in group rings with $G$-adapted coefficient rings, Canad. Math. Bull., (1) 48 (2005), 80-89. MR 2118765
  • 2. G. Higman, The units of group-rings, Proc. London Math. Soc., (2)46, (1940), 231 - 248. MR 0002137 (2:5b)
  • 3. K. Ireland and M. Rosen, A Classical Introduction to Modern Number Theory, 2nd Ed., Springer-Verlag, 1990. MR 1070716 (92e:11001)
  • 4. M. Mazur, Groups normal in the unit groups of their group rings, preprint.
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Additional Information

Allen Herman
Affiliation: Department of Mathematics and Statistics, University of Regina, Regina, Saskatchewan, Canada S4S 0A2

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

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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