Endomorphisms preserving coordinates of polynomial algebras
Commutative Algebra
2011-10-25 v3 Algebraic Geometry
Rings and Algebras
Abstract
It is proved that the Jacobian of a k-endomorphism of k[x_1,...,x_n] over a field k of characteristic zero taking every tame coordinate to a coordinate, must be a nonzero constant in k. It is also proved that the Jacobian of an R-endomorphism of A:=R[x_1,...,x_n] (where R is a polynomial ring in finite number of variables over an infinite field k), taking every R-linear coordinate of A to an R-coordinate of A, is a nonzero constant in k.
Cite
@article{arxiv.1110.4317,
title = {Endomorphisms preserving coordinates of polynomial algebras},
author = {Yun-Chang Li and Jie-Tai Yu},
journal= {arXiv preprint arXiv:1110.4317},
year = {2011}
}
Comments
6 pages