Conditions satisfied by characteristic polynomials in fields and division algebras

Details Conditions satisfied by characteristic polynomials in fields and division algebras Conditions satisfied by characteristic polynomials in fields and division algebras

2000-02-22

arxiv.org/abs/math/0002176v1

Mathematics

Algebraic Geometry

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

Scientific paper

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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