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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Algebraic elements in group rings


Authors: I. B. S. Passi and D. S. Passman
Journal: Proc. Amer. Math. Soc. 108 (1990), 871-877
MSC: Primary 20C07; Secondary 16A27, 46L99
MathSciNet review: 1007508
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Abstract: In this brief note, we study algebraic elements in the complex group algebra $ {\mathbf{C}}[G]$. Specifically, suppose $ \xi \in {\mathbf{C}}[G]$ satisfies $ f(\xi ) = 0$ for some nonzero polynomial $ f(x) \in {\mathbf{C}}[x]$. Then we show that a certain fairly natural function of the coefficients of $ \xi $ is bounded in terms of the complex roots of $ f(x)$. For $ G$ finite, this is a recent observation of [HLP]. Thus the main thrust here concerns infinite groups, where the inequality generalizes results of [K] and [W] on traces of idempotents.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1990-1007508-2
PII: S 0002-9939(1990)1007508-2
Article copyright: © Copyright 1990 American Mathematical Society