Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Conditions satisfied by characteristic polynomials in fields and
  division algebras   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.

33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
19
The categories of this paper are: eess
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
17
The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th