Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rank one discrete valuations of power series fields   In this paper we study the rank one discrete valuations of the field
$k((X_1,..., X_n))$ whose center in $k\lcor\X\rcor$ is the maximal ideal. In
sections 2 to 6 we give a construction of a system of parametric equations
describing such valuations. This amounts to finding a parameter and a field of
coefficients. We devote section 2 to finding an element of value 1, that is, a
parameter. The field of coefficients is the residue field of the valuation, and
it is given in section 5.
  The constructions given in these sections are not effective in the general
case, because we need either to use the Zorn's lemma or to know explicitly a
section $\sigma$ of the natural homomorphism $R_v\to\d$ between the ring and
the residue field of the valuation $v$.
  However, as a consequence of this construction, in section 7, we prove that
$k((\X))$ can be embedded into a field $L((\Y))$, where $L$ is an algebraic
extension of $k$ and the {\em ``extended valuation'' is as close as possible to
the usual order function}.

16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
15
The categories of this paper are: nucl-ex
18
The categories of this paper are: econ
37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
1
The categories of this paper are: cs
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
17
The categories of this paper are: q-fin