A short and elementary proof of Jung's theorem

TL;DR

This paper presents a concise and straightforward proof of Jung's theorem, demonstrating that automorphisms of polynomial rings over characteristic zero fields are generated by elementary and linear automorphisms.

Contribution

It provides a simplified and elementary proof of Jung's theorem, enhancing understanding of automorphism groups of polynomial rings.

Findings

Automorphisms of K[x,y] are generated by elementary and linear automorphisms.

The proof is shorter and more elementary than previous proofs.

The result applies to fields of characteristic zero.

Abstract

We give a short and elementary proof of Jung's theorem, which states that for a field K of characteristic zero the automorphisms of K[x,y] are generated by elementary automorphisms and linear automorphisms.