  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.
