# The Jacobian conjecture and the degree of field extension

#### Abstract

Let k be an algebraically closed field of characteristic zero. If two polynomials $f(x,y)$ and $g(x,y)$ satisfy the Jacobian condition $f\sb{x}g\sb{y} - f\sb{y}g\sb{x}\ \in\ k\sp{*}$, then the degree of the field extension of $k(x,y)$ over $k(f,g), \lbrack k(x,y):k(f,g)\rbrack,$ is less than or equal to the minimum of deg f and deg g.

#### Degree

Ph.D.

Moh, Purdue University.

#### Subject Area

Mathematics

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