Algebraic elements in group rings

Abstract

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