Conditions satisfied by characteristic polynomials in fields and division algebras

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.

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