Test elements, retracts and automorphic orbits

Details Test elements, retracts and automorphic orbits Test elements, retracts and automorphic orbits

2008-07-07

arxiv.org/abs/0807.1142v1

Mathematics

Rings and Algebras

11 pages

Scientific paper

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.

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