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Conditions satisfied by characteristic polynomials in fields and division algebras

Zinovy Reichstein·Boris Youssin
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Abstract

Suppose E/F is a field extension. We ask whether or not there exists an element of E whose characteristic polynomial has one or more zero coefficients in specified positions. We show that the answer is frequently ``no''. We also prove similar results for division algebras and show that the universal division algebra of degree n does not have an element of trace 0 and norm 1.

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Zinovy Reichstein, Boris Youssin. 2000-02-22. Conditions satisfied by characteristic polynomials in fields and division algebras. https://arxiv.org/abs/math/0002176

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