✦ LIBER ✦

Conditions satisfied by characteristic polynomials in fields and division algebras

✍ Scribed by Z. Reichstein; B. Youssin

Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 219 KB
Volume: 166
Category: Article
ISSN: 0022-4049
DOI: 10.1016/s0022-4049(01)00009-3

No coin nor oath required. For personal study only.

✦ Synopsis

Suppose E=F is a ÿeld extension. We ask whether or not there exists an element of E whose characteristic polynomial has one or more zero coe cients in speciÿed 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.