Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Primitive Element Theorem for Fields with Commuting Derivations and
  Automorphisms   We establish a Primitive Element Theorem for fields equipped with several
commuting operators such that each of the operators is either a derivation or
an automorphism. More precisely, we show that for every extension $F \subset E$
of such fields of zero characteristic such that
  $\bullet$ $E$ is generated over $F$ by finitely many elements using the field
operations and the operators,
  $\bullet$ every element of $E$ satisfies a nontrivial equation with
coefficient in $F$ involving the field operations and the operators,
  $\bullet$ the action of the operators on $E$ is irredundant there exists an
element $a \in E$ such that $E$ is generated over $F$ by $a$ using the field
operations and the operators.
  This result generalizes the Primitive Element Theorems by Kolchin and Cohn in
two directions simultaneously: we allow any numbers of derivations and
automorphisms and do not impose any restrictions on the base field $F$.

27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
14
The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat