English

Test elements, retracts and automorphic orbits

Rings and Algebras 2008-07-09 v1

Abstract

Let A2A_2 be a free associative or polynomial algebra of rank two over a field KK of characteristic zero. Based on the degree estimate of Makar-Limanov and J.-T.Yu, we prove: 1) An element pA2p \in A_2 is a test element if pp does not belong to any proper retract of A2A_2; 2) Every endomorphism preserving the automorphic orbit of a nonconstant element of A2A_2 is an automorphism.

Keywords

Cite

@article{arxiv.0807.1142,
  title  = {Test elements, retracts and automorphic orbits},
  author = {Sheng-Jun Gong and Jie-Tai Yu},
  journal= {arXiv preprint arXiv:0807.1142},
  year   = {2008}
}

Comments

11 pages

R2 v1 2026-06-21T10:58:18.262Z