STABLY CO-TAME POLYNOMIAL AUTOMORPHISMS OVER COMMUTATIVE RINGS

@article{Kuroda2016STABLYCP,
  title={STABLY CO-TAME POLYNOMIAL AUTOMORPHISMS OVER COMMUTATIVE RINGS},
  author={Shigeru Kuroda},
  journal={Transformation Groups},
  year={2016},
  volume={22},
  pages={1031-1040}
}
  • S. Kuroda
  • Published 2016
  • Mathematics
  • Transformation Groups
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 this paper, we give conditions for stable co-tameness of polynomial automorphisms. 
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References

SHOWING 1-10 OF 14 REFERENCES
GENERALISATIONS OF THE TAME AUTOMORPHISMS OVER A DOMAIN OF POSITIVE CHARACTERISTIC
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 newExpand
Stable tameness of two-dimensional polynomial automorphisms over a regular ring
Abstract In this paper it is established that all two-dimensional polynomial automorphisms over a regular ring R are stably tame. This results from the main theorem of this paper, which asserts thatExpand
The affine automorphism group of A^3 is not a maximal subgroup of the tame automorphism group
We construct explicitly a family of proper subgroups of the tame automorphism group of affine three-space (in any characteristic) which are generated by the affine subgroup and a non-affine tameExpand
On Generators of the Tame Invertible Polynomial Maps Group
TLDR
The group TGAn of tame invertible polynomial maps is generated by the affine group AGLn and the triangular polynomic maps group Bn and some classes of polynometric maps q, which have the same property are ascertained. Expand
Polynomial automorphisms over finite fields: Mimicking non-tame and tame maps by the Derksen group.
If F is a polynomial automorphism over a finite field Fq in dimen- sion n, then it induces a bijectionqr(F) of (Fqr) n for every r 2 N � . We say that F can be 'mimicked' by elements of a certainExpand
The tame and the wild automorphisms of polynomial rings in three variables
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 τ ∈Expand
Polynomial Automorphisms and the Jacobian Conjecture
In this paper we give an update survey of the most important results concerning the Jacobian conjecture: several equivalent descriptions are given and various related conjectures are discussed. AtExpand
Coordinates of R[x,y]: Constructions and Classifications
Let R be a PID. We construct and classify all coordinates of R[x, y] of the form p 2 y + Q 2(p 1 x + Q 1(y)) with p 1, p 2 ∈ qt(R) and Q 1, Q 2 ∈ qt(R)[y]. From this construction (with R = K[z]) weExpand
On automorphism group of k[x, y]
Stably Derksen polynomial automorphisms over finite fields (Japanese)
  • Master’s Thesis,
  • 2016
...
1
2
...