Abstract
Throughout this chapter R denotes a commutative ring, however in almost all results R will be a domain, and R[X]:= R[X1,…, X n ] the polynomial ring in n variables over R. We will consider the following subgroups of AutR R [X]: Aff(R, n):= the affine subgroup of AutR R[X] consisting of all R-automorphisms F such that deg F i = 1 for all i. J(R,n):= the “de Jonquières” subgroup of AutR R[X] consisting of all R-automorphisms F of the form
where each a i belongs to R* and f i ∈ R [X i +1,… X n ] for all 1 ≤ i ≤ n - 1 and f n ∈ R. E (R, n):= the subgroup of Aut R R[X] generated by the elementary automorphisms, i.e. the automorphisms of the form
for some \(a \in R\left[ {{X_1}, \ldots,{{\hat X}_i}, \ldots,{X_n}} \right]\) and 1 ≤ i ≤ n.
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© 2000 Springer Basel AG
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van den Essen, A. (2000). The tame automorphism group of a polynomial ring. In: Polynomial Automorphisms. Progress in Mathematics, vol 190. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8440-2_5
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DOI: https://doi.org/10.1007/978-3-0348-8440-2_5
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9567-5
Online ISBN: 978-3-0348-8440-2
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