Article ID Journal Published Year Pages File Type
4583744 Journal of Algebra 2016 9 Pages PDF
Abstract

Given an integral domain A we consider the set of all integral elements over A that can occur as an eigenvalue of a symmetric matrix over A. We give a sufficient criterion for being such an element. In the case where A is the ring of integers of an algebraic number field this sufficient criterion is also necessary and we show that the size of matrices grows linearly in the degree of the element. The latter result settles a questions raised by Bass, Estes and Guralnick.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory
Authors
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