Stably co-tame polynomial automorphisms over commutative rings

TL;DR

This paper introduces the concept of stably co-tame polynomial automorphisms over commutative rings, providing conditions for their identification and understanding their relation to tame automorphisms.

Contribution

It defines stably co-tame automorphisms and establishes criteria for their co-tameness over commutative rings.

Findings

Provides conditions for stably co-tameness

Connects stably co-tame automorphisms with tame automorphisms

Advances understanding of polynomial automorphism structure

Abstract

We say that a polynomial automorphism $\phi $ in $n$ variables is stably co-tame if the tame subgroup in $n$ variables is contained in the subgroup generated by $\phi $ and affine automorphisms in $n+1$ variables. In this paper, we give conditions for stably co-tameness of polynomial automorphisms.