Abhyankar–Moh theorem

In mathematics, the Abhyankar–Moh theorem states that if $L$ is a complex line in the complex affine plane $\mathbb{C}^2$ , then every embedding of $L$ into $\mathbb{C}^2$ 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.

References

Abhyankar, Shreeram S.; Moh, Tzuong-Tsieng (1975), "Embeddings of the line in the plane", Journal für die reine und angewandte Mathematik, 276: 148–166, MR 0379502 .
M. Hazewinkel (2001) [1994], "Abhyankar–Moh theorem", in Hazewinkel, Michiel, Encyclopedia of Mathematics, Springer Science+Business Media B.V. / Kluwer Academic Publishers, ISBN 978-1-55608-010-4

This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.