References
H. W. E. Jung, “Über ganze birationale Transformationen der Ebene,” J. Reine Angew. Math.,184, 161–174 (1942).
W. Van der Kulk, “On polynomial rings in two variables,” Nieuw Arch. Wisk., No. 1, 33–41 (1953).
M. K. Smith, “Stably tame automorphisms,” J. Pure Appl. Algebra,58, 209–212 (1989).
A. J. Czerniakiewicz, “Automorphisms of a free associative algebra of rank two. II,” Trans. Amer. Math. Soc,171, 309–315 (1972).
L. G. Makar-Limanov, “Automorphisms of free algebras with two generators,” Funktsional. Analiz i Prilozhen., No. 4, 107–108 (1970).
G. M. Bergman and W. Dicks, “On universal derivations,” J. Algebra,36, 193–211 (1975).
J. Lewin, “A matrix representation for associative algebras. I,” Trans. Amer. Math. Soc,188, 293–308 (1974).
W. Dicks and J. Lewin, “Jacobian conjecture for free associative algebras,” Comm. Algebra,10, No. 12, 1285–1306 (1982).
U. U. Umirbaev, “Partial derivatives and endomorphisms of some relatively free Lie algebras,” Sibirsk. Mat. Zh.,34, No. 6, 179–188 (1993).
V. A. Artamonov, “Projective metabelian groups and Lie algebras,” Izv. Akad. Nauk SSSR Ser. Mat.,42, No. 2, 226–236 (1978).
Author information
Authors and Affiliations
Additional information
Translated fromSibirskii Matematicheskii Zhurnal, Vol. 36, No. 4, pp. 911–916, July–August, 1995.
In conclusion, the author expresses his gratitude to Professor I. P. Shestakov for the interest evinced.
Rights and permissions
About this article
Cite this article
Umirbaev, U.U. On the extension of automorphisms of polynomial rings. Sib Math J 36, 787–791 (1995). https://doi.org/10.1007/BF02107336
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02107336