Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Absence of algebraic relations and of zero divisors under the assumption
  of finite non-microstates free Fisher information   We show that in a tracial and finitely generated $W^\ast$-probability space
existence of conjugate variables in an appropriate sense exclude algebraic
relations for the generators. Moreover, under the assumption of finite
non-microstates free Fisher information, we prove that there are no zero
divisors in the sense that the product of any non-commutative polynomial in the
generators with any element from the von Neumann algebra is zero if and only if
at least one of those factors is zero.

20
The categories of this paper are: acc-phys
30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio