%0 Journal Article
%T Test elements, retracts and automorphic orbits
%A Sheng-Jun Gong
%A Jie-Tai Yu
%J Mathematics
%D 2008
%I arXiv
%X Let $A_2$ 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 $p \in A_2$ is a test element if $p$ does not belong to any proper retract of $A_2$; 2) Every endomorphism preserving the automorphic orbit of a nonconstant element of $A_2$ is an automorphism.
%U http://arxiv.org/abs/0807.1142v1