Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Supertropical algebra   We develop the algebraic polynomial theory for "supertropical algebra," as
initiated earlier over the real numbers by the first author. The main
innovation there was the introduction of "ghost elements," which also play the
key role in our structure theory. Here, we work somewhat more generally over an
ordered monoid, and develop a theory which contains the analogs of several
basic theorems of classical commutative algebra. This structure enables one to
develop a Zariski-type algebraic geometric approach to tropical geometry,
viewing tropical varieties as sets of roots of (supertropical) polynomials,
leading to an analog of the Hilbert Nullstellensatz. Particular attention is
paid to factorization of polynomials. In one indeterminate, any polynomial can
be factored into linear and quadratic factors, and unique factorization holds
in a certain sense. On the other hand, the failure of unique factorization in
several indeterminates is explained by geometric phenomena described in the
paper.

12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
14
The categories of this paper are: math-ph
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin