Abhyankar–Moh theorem

In mathematics, the Abhyankar–Moh theorem states that if ${\displaystyle L}$ is a complex line in the complex affine plane ${\displaystyle \mathbb {C} ^{2}}$, then every embedding of ${\displaystyle L}$ into ${\displaystyle \mathbb {C} ^{2}}$ extends to an automorphism of the plane. It is named after Shreeram Shankar Abhyankar and Tzuong-Tsieng Moh, who published it in 1975. More generally, the same theorem applies to lines and planes over any algebraically closed field of characteristic zero, and to certain well-behaved subsets of higher-dimensional complex affine spaces.