Test elements, retracts and automorphic orbits

2008/07/07 by Sheng-Jun Gong, Gong, Sheng-Jun, Jie-Tai Yu +1
Mathematics · Physics and Astronomy · #13F20 (Secondary) #16S10 #16W20 (Primary) 13B10 #Advanced Differential Equations and Dynamical Systems #FOS: Mathematics #Geometric and Algebraic Topology #Quantum chaos and dynamical systems #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.0807.1142

openalex publication_date 2008/07/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let A₂ be a free associative or polynomial algebra of rank two over a field K of characteristic zero. Based on the degree estimate of Makar-Limanov and J.-T.Yu, we prove: 1) An element p ∈ A₂ is a test element if p does not belong to any proper retract of A₂; 2) Every endomorphism preserving the automorphic orbit of a nonconstant element of A₂ is an automorphism.

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