English

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.

Keywords

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