Geodesic
The Jacobian Conjecture for the free associative algebra (of~arbitrary characteristic)
Čebyševskij sbornik, Tome 20 (2019) no. 3, pp. 390-393

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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. 
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     author = {A. Belov-Kanel and L. Rowen and Jie-Tai Yu},
     title = {The {Jacobian} {Conjecture} for the free associative algebra (of~arbitrary characteristic)},
     journal = {\v{C}eby\v{s}evskij sbornik},
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A. Belov-Kanel; L. Rowen; Jie-Tai Yu. The Jacobian Conjecture for the free associative algebra (of~arbitrary characteristic). Čebyševskij sbornik, Tome 20 (2019) no. 3, pp. 390-393. http://geodesic.mathdoc.fr/item/CHEB_2019_20_3_a25/