chebЧебышевский сборникChebyshevskii Sbornik2226-8383Tula State Lev Tolstoy Pedagogical University10.22405/2226-8383-2019-20-3-390-393cheb-729Research ArticleКраткие сообщенияГипотеза Якобиана для свободной ассоциативной алгебры (произвольной характеристики)The Jacobian Conjecture for the free associative algebra (of arbitrary characteristic)Белов-КанельАлексей ЯковлевичBelov-KanelAlexei Yakovlevichbeloval@cs.biu.ac.ilРовенЛуи ХейлRowenLouis Hailerowen@math.biu.ac.ilЦзе-ТайЮйJie-TaiYujietai@hotmail.com201905032020203390393Copyright © Белов-Канель А.Я., Ровен Л., Цзе-Тай Ю., 20202020Белов-Канель А.Я., Ровен Л., Цзе-Тай Ю.Belov-Kanel A.Y., Rowen L., Jie-Tai Y.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://www.chebsbornik.ru/jour/article/view/729

Целью данной работы является использование PI-теории для упрощения результатов Дикса и Левина [4] об автоморфизмах свободной алгебры F{X}, а именно: если якобиан обратим, тогда каждый эндоморфизм является эпиморфизмом. Результаты переносятся на широкий класс колец.

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.

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The authors declare that there are no conflicts of interest present.