Endomorphisms preserving coordinates of polynomial algebras

Details Endomorphisms preserving coordinates of polynomial algebras Endomorphisms preserving coordinates of polynomial algebras

2011-10-19

arxiv.org/abs/1110.4317v3

Mathematics

Commutative Algebra

6 pages

Scientific paper

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.

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