A short proof that the free associative algebra is Hopfian
arXiv:1708.04361
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.
arXiv comment5 pages, Shengeng University and Bar-Ilan University