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Trivial units for group rings over rings of algebraic integers

Author(s): Allen Herman; Yuanlin Li
Journal: Proc. Amer. Math. Soc. 134 (2006), 631-635.
MSC (2000): Primary 16S34; Secondary 16U60
Posted: July 18, 2005
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Abstract: Let be a nontrivial torsion group and be the ring of integers of an algebraic number field. The necessary and sufficient conditions are given under which has only trivial units.

References:

1.: A. Herman, Y. Li and M.M. Parmenter, Trivial units in group rings with -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.
5.: C. Polcino Milies and S.K. Sehgal, An Introduction to Group Rings, Kluwer Academic Publishers, Dordrecht, 2002. MR 1896125 (2003b:16026)

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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: 10.1090/S0002-9939-05-08018-4
PII: S 0002-9939(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
Posted: 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
Copyright of article: Copyright 2005, American Mathematical Society


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