Geodesic
Endomorphisms of free associative algebras over commutative rings and their Jacobian matrices
Fundamentalʹnaâ i prikladnaâ matematika, Tome 1 (1995) no. 1, pp. 177-189.

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A matrix criterion for an endomorphism of the free associative algebra of finite rank over a commutative ring with the unity element to be an automorphism is obtained. 
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A. A. Zolotykh; A. A. Mikhalev. Endomorphisms of free associative algebras over commutative rings and their Jacobian matrices. Fundamentalʹnaâ i prikladnaâ matematika, Tome 1 (1995) no. 1, pp. 177-189. http://geodesic.mathdoc.fr/item/FPM_1995_1_1_a8/

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