Stable tameness of automorphisms of F<x,y,z> fixing z

TL;DR

This paper proves that all automorphisms fixing z in the free associative algebra over any field are stably tame, advancing understanding of automorphism structures in algebra.

Contribution

It establishes that every z-automorphism of the free associative algebra is stably tame, a significant step in automorphism theory.

Findings

All z-automorphisms are stably tame.

Results hold over arbitrary fields.

Enhances understanding of automorphism structure.

Abstract

It is proved that every z-automorphism (z-coordinate, respectively) of the free associative algebra F<x,y,z> over an arbitrary field F is stably tame.