Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Elements of Algebraic Geometry and the Positive Theory of Partially
  Commutative Groups   In this version small mistakes are corrected and the exposition is changed as
suggested by the referee (to appear in Canadian Journal of Mathematics).
  The first main result of the paper is a criterion for a partially commutative
group $\GG$ to be a domain. It allows us to reduce the study of algebraic sets
over $\GG$ to the study of irreducible algebraic sets, and reduce the
elementary theory of $\GG$ (of a coordinate group over $\GG$) to the elementary
theories of the direct factors of $\GG$ (to the elementary theory of coordinate
groups of irreducible algebraic sets).
  Then we establish normal forms for quantifier-free formulas over a
non-abelian directly indecomposable partially commutative group $\HH$.
Analogously to the case of free groups, we introduce the notion of a
generalised equation and prove that the positive theory of $\HH$ has quantifier
elimination and that arbitrary first-order formulas lift from $\HH$ to $\HH\ast
F$, where $F$ is a free group of finite rank. As a consequence, the positive
theory of an arbitrary partially commutative group is decidable.

34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
19
The categories of this paper are: eess
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
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The categories of this paper are: bayes-an
23
The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
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The categories of this paper are: q-alg
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The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat