Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ideas about the Jacobian Conjecture   Let $F:\mathbb{C}[x_1,\ldots,x_n] \to \mathbb{C}[x_1,\ldots,x_n]$ be a
$\mathbb{C}$-algebra endomorphism that has an invertible Jacobian. We bring two
ideas concerning the Jacobian Conjecture: First, we conjecture that for all
$n$, the degree of the field extension $\mathbb{C}(F(x_1),\ldots,F(x_n))
\subseteq \mathbb{C}(x_1,\ldots,x_n)$ is less than or equal to $d^{n-1}$, where
$d$ is the minimum of the degrees of the $F(x_i)$'s. If this conjecture is
true, then the generalized Jacobian Conjecture is true. Second, we suggest to
replace in some known theorems the assumption on the degrees of the $F(x_i)$'s
by a similar assumption on the degrees of the minimal polynomials of the
$x_i$'s over $\mathbb{C}(F(x_1)\ldots,f(x_n))$; this way we obtain some
analogous results to the known ones.

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The categories of this paper are: quant-ph
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The categories of this paper are: patt-sol
1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph
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The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
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The categories of this paper are: nlin
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The categories of this paper are: q-fin
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The categories of this paper are: adap-org
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The categories of this paper are: comp-gas
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The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
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The categories of this paper are: plasm-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: funct-an