Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dominance and Transmissions in Supertropical Valuation Theory   This paper is a sequel of [IKR1], where we defined supervaluations on a
commutative ring $R$ and studied a dominance relation $\phi \geq \psi$ between
supervaluations $\phi$ and $\psi$ on $R$, aiming at an enrichment of the
algebraic tool box for use in tropical geometry.
  A supervaluation $\phi:R \to U$ is a multiplicative map from $R$ to a
supertropical semiring $U$, cf. [IR1], [IR2], [IKR1], with further properties,
which mean that $\phi$ is a sort of refinement, or covering, of an m-valuation
(= monoid valuation) $v: R \to M$. In the most important case, that $R$ is a
ring, m-valuations constitute a mild generalization of valuations in the sense
of Bourbaki [B], while $\phi \geq \psi$ means that $\psi: R \to V$ is a sort of
coarsening of the supervaluation $\phi$. If $\phi(R)$ generates the semiring
$U$, then $\phi \geq \psi$ iff there exists a "transmission" $\alpha: U \to V$
with $\psi = \alpha \circ \phi$.
  Transmissions are multiplicative maps with further properties, cf. [IKR1,
Sec. 5]. Every semiring homomorphism $\alpha: U \to V$ is a transmission, but
there are others which lack additivity, and this causes a major difficulty. In
the main body of the paper we study surjective transmissions via equivalence
relations on supertropical semirings, often much more complicated than
congruences by ideals in usual commutative algebra.

28
The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
14
The categories of this paper are: math-ph
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
10
The categories of this paper are: q-bio