Locally nilpotent derivations and the structure of rings

TL;DR

This paper explores the structure of certain algebraic rings by analyzing the kernels of locally nilpotent derivations, providing insights into their properties and classifications.

Contribution

It introduces new methods for understanding the structure of rings via locally nilpotent derivations in characteristic zero.

Findings

Characterization of kernels of locally nilpotent derivations

Structural insights into commutative integral domains

Potential classification results for rings based on derivations

Abstract

We investigate the structure of commutative integral domains $B$ of characteristic zero by studying the kernels of locally nilpotent derivations $D : B \to B$.