Conditions satisfied by characteristic polynomials in fields and division algebras

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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.
AMS LaTeX 1.1, 22 pages. Author-supplied dvi file available at http://ucs.orst.edu/~reichstz/pub.html

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Algebraic Geometry, Rings and Algebras

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http://salesiana.dossiersoluciones.com/handle/123456789/58737

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0002176
 http://arxiv.org/abs/math/0002176

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arXiv