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 Chebyshevskii Sb., 2019, Volume 20, Issue 3, Pages 390–393 (Mi cheb819)

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The Jacobian Conjecture for the free associative algebra (of arbitrary characteristic)

A. Belov-Kanelab, L. Rowenc, Jie-Tai Yude

a College of Mathematics and Statistics, Shenzhen University, Shenzhen, 518061, China
b Bar-Ilan University (Ramat Gan, Israel)
c Department of Mathematics, Bar-Ilan University (Israel)
d MIPT
e Department of Mathematics, Sengeng University (China)

Abstract: The object of this note is to use PI-theory to simplify the results of Dicks and Lewin [4] on the automorphisms of the free algebra $F\{ X\}$, namely that if the Jacobian is invertible, then every endomorphism is an epimorphism. We then show how the same proof applies to a somewhat wider class of rings.

Keywords: Automorphisms, polynomial algebras, free associative algebras.

DOI: https://doi.org/10.22405/2226-8383-2018-20-3-390-393

Full text: PDF file (556 kB)

UDC: 512
Accepted:12.11.2019
Language:

Citation: A. Belov-Kanel, L. Rowen, Jie-Tai Yu, “The Jacobian Conjecture for the free associative algebra (of arbitrary characteristic)”, Chebyshevskii Sb., 20:3 (2019), 390–393

Citation in format AMSBIB
\Bibitem{KanRowYu19} \by A.~Belov-Kanel, L.~Rowen, Jie-Tai~Yu \paper The Jacobian Conjecture for the free associative algebra (of~arbitrary characteristic) \jour Chebyshevskii Sb. \yr 2019 \vol 20 \issue 3 \pages 390--393 \mathnet{http://mi.mathnet.ru/cheb819} \crossref{https://doi.org/10.22405/2226-8383-2018-20-3-390-393}