Algebraic elements in group rings

Author:

Passi I. B. S.,Passman D. S.

Abstract

In this brief note, we study algebraic elements in the complex group algebra C [ G ] {\mathbf {C}}[G] . Specifically, suppose ξ C [ G ] \xi \in {\mathbf {C}}[G] satisfies f ( ξ ) = 0 f(\xi ) = 0 for some nonzero polynomial f ( x ) C [ x ] f(x) \in {\mathbf {C}}[x] . Then we show that a certain fairly natural function of the coefficients of ξ \xi is bounded in terms of the complex roots of f ( x ) f(x) . For G 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.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference6 articles.

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1. Group algebras;Indian Journal of Pure and Applied Mathematics;2012-04

2. On the trace of idempotent matrices over group algebras;Mathematische Zeitschrift;2006-03-31

3. Algebraic Elements in Group Rings;Current Trends in Number Theory;2002

4. Semisimple elements in group algebras;Communications in Algebra;1993-01

5. Torsion units in matrix group rings;Communications in Algebra;1992-01

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