#### 100 Citations

The Nagata Type Polynomial Automorphisms and Rectifiable Space Lines

- Mathematics
- 2014

We find a remarkable relation between the Nagata type polynomial automorphisms and rectifiable space lines of a certain form.

Length Four Polynomial Automorphisms

- Mathematics
- 2008

We study the structure of length four polynomial automorphisms of R[X, Y] when R is a unique factorization domain. The results from this study are used to prove that, if SL m (R[X 1, X 2,…, X n ]) =… Expand

Multidegrees of tame automorphisms of C^n

- Mathematics
- 2011

Let F=(F_1,...,F_n):C^n --> C^n be a polynomial mapping. By the multidegree of the mapping F we mean mdeg F=(deg F_1,...,deg F_n), an element of N^n.
The aim of this paper is to study the following… Expand

The Nagata automorphism is wild

- Mathematics, Medicine
- Proceedings of the National Academy of Sciences of the United States of America
- 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 of… Expand

A new co-tame automorphism of the polynomial ring

- Mathematics
- 2020

In this paper, we discuss subgroups of the automorphism group of the polynomial ring in n variables over a field of characteristic zero. An automorphism F is said to be {\it co-tame} if the subgroup… Expand

A non-tame and non-co-tame automorphism of the polynomial ring

- Mathematics
- 2020

An automorphism $F$ of the polynomial ring in $n$ variables over a field of characteristic zero is said to be {\it co-tame} if the subgroup of the automorphism group of the polynomial ring generated… Expand

STABLY CO-TAME POLYNOMIAL AUTOMORPHISMS OVER COMMUTATIVE RINGS

- Mathematics
- 2016

We say that a polynomial automorphism ϕ in n variables is stably co-tame if the tame subgroup in n variables is contained in the subgroup generated by ϕ and affine automorphisms in n+1 variables. In… Expand

GENERALISATIONS OF THE TAME AUTOMORPHISMS OVER A DOMAIN OF POSITIVE CHARACTERISTIC

- Mathematics
- 2013

In this paper, we introduce two generalizations of the tame subgroup of the automorphism group of a polynomial ring over a domain of positive characteristic. We study detailed structures of these new… Expand

The tame automorphism group in two variables over basic Artinian rings

- Mathematics
- 2010

In a recent paper it has been established that over an Artinian ring R all two-dimensional polynomial automorphisms having Jacobian determinant one are tame if R is a Q-algebra. This is a… Expand

Actions of $SL_2(k)$ on affine $k$-domains and fundamental pairs

- Mathematics
- 2021

Working over a field k of characteristic zero, this paper studies algebraic actions of SL2(k) on affine k-domains by defining and investigating fundamental pairs of derivations. There are three main… Expand