Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A strong version of implicit function theorem   We suggest the necessary/sufficient criteria for the existence of a
(order-by-order) solution y(x) of a functional equation F(x,y)=0 over a ring.
In full generality, the criteria hold in the category of filtered groups, this
includes the wide class of modules over (commutative, associative) rings. The
classical implicit function theorem and its strengthening obtained by Tougeron
and Fisher appear to be (weaker) particular forms of the general criterion.
  We obtain a special criterion for solvability of the equations arising from
group actions, g(w)=w+u, here u is "small". As an immediate application we
re-derive the classical criteria of determinacy, in terms of the tangent space
to the orbit.
  Finally, we prove the Artin-Tougeron-type approximation theorem: if a system
of C^\infty-equations has a formal solution and the derivative satisfies a
Lojasiewicz-type condition then the system has a C^\infty-solution.

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The categories of this paper are: hep-ph
16
The categories of this paper are: stat
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg