Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A proof of Zhil'tsov's theorem on decidability of equational theory of
  epigroups   Epigroups are semigroups equipped with an additional unary operation called
pseudoinversion. Each finite semigroup can be considered as epigroup. We prove
the following theorem announced by Zhil'tsov in 2000: the equational theory of
the class of all epigroups coincides with the equational theory of the class of
all finite epigroups and is decidable. We show that the theory is not finitely
based but provide a transparent infinite basis for it.

28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph
19
The categories of this paper are: eess
23
The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex