2012/06/22 by Yunchang Li, Li, Yun-Chang
Mathematics · #Advanced Differential Equations and Dynamical Systems #FOS: Mathematics #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.1206.5085
openalex publication_date 2012/06/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let K be a field of characteristic zero, K[x,y] be the polynomial ring in two variables. Let ϕ=(f, g) be an endomorphism of K[x,y]. It is proved that if ϕ maps each coordinate to a generator of some proper retract, then it is an automorphism. As a corollary, the retract preserving problem is solved for both polynomial ring over K and free algebra over an arbitrary field when n=2.