Let $S$ and $T$ be polynomial rings over a field of characteristic zero in
finitely many variables. Assume that $T$ is an unramified extension of $S$ with
$T^\times = k^\times$. Then $T = S$.In this paper, the Jacobian Conjecture is
proved in the abstract way instead of treating variables in a polynomial ring.
Let $S$ and $T$ be polynomial rings over a field of characteristic zero in
finitely many variables. Assume that $T$ is an unramified extension of $S$ with
$T^\times = k^\times$. Then $T = S$.In this paper, the Jacobian Conjecture is
proved in the abstract way instead of treating variables in a polynomial ring.