# Abhyankar–Moh theorem

Short description: Every embedding of a complex line into the complex affine plane extends to an automorphism

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.