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Z. Reichstein, B. Youssin, * Conditions satisfied by characteristic
polynomials in fields and division algebras *, J. Pure
Applied Algebra, 166 (2002), 165-184.

**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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