A short proof that the free associative algebra is Hopfian
Rings and Algebras
2020-01-14 v3
Abstract
A short proof is given of the fact that various classes of algebras including the free associative algebra are Hopfian, i.e., every epimorphism is an automorphism. This further simplifies the Dicks-Lewin solution of the Jacobian conjecture for the free associative algebra.
Cite
@article{arxiv.1708.04361,
title = {A short proof that the free associative algebra is Hopfian},
author = {Alexei Kanel-Belov and Louis Rowen and Jie-Tai Yu},
journal= {arXiv preprint arXiv:1708.04361},
year = {2020}
}
Comments
5 pages, Shengeng University and Bar-Ilan University