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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
Posted:
July 18, 2005
MathSciNet review:
2180878
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Additional Information
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:
http://dx.doi.org/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
Article copyright:
© Copyright 2005 American Mathematical Society
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