Let C = F [x1, x2, . . . , xn] be the polynomial ring in the variables x1, x2, . . . , xn over a field F , and let AutC be the group of automorphisms of C as an algebra over F . An automorphism Ï„ âˆˆâ€¦ (More)

Proceedings of the National Academy of Sciencesâ€¦

2004

It is proved that there exist wild coordinates in the polynomial algebra in three variables over a field of characteristic zero. This result implies the famous Nagata conjecture.

We describe a set of defining relations of the tame automorphism group T A 3 (F) of the polynomial algebra F [x 1 , x 2 , x 3 ] in variables x 1 , x 2 , x 3 over an arbitrary field F ofâ€¦ (More)

Proceedings of the National Academy of Sciencesâ€¦

2003

It is proved that the well known Nagata automorphism of the polynomial ring in three variables over a field of characteristic zero is wild, that is, it can not be decomposed into a product ofâ€¦ (More)

We describe a set of defining relations for automorphism groups of finitely generated free algebras of Nielsen-Schreier varieties. In particular, this gives a representation of the automorphismâ€¦ (More)