A. Belov-Kanel, L. Rowen, Jie-Tai Yu, “The Jacobian Conjecture for the free associative algebra (of arbitrary characteristic)”, Chebyshevskii Sb., 2019, Volume 20, Issue 3,Pages <nobr>390

BRIEF MESSAGE

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

A. Belov-Kanel^ab, L. Rowen^c, Jie-Tai Yu^de

^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.

UDC: 512

Received: 16.10.2019
Accepted: 12.11.2019

Language: English

DOI: 10.22405/2226-8383-2018-20-3-390-393