Strongly \'etale difference algebras and Babbitt's decomposition

TL;DR

This paper introduces strongly étale difference algebras, analogous to étale algebras in algebra, and uses them to improve Babbitt's decomposition theorem with applications to difference algebraic groups and compatibility issues.

Contribution

It defines strongly étale difference algebras and provides an improved Babbitt's decomposition theorem with new applications.

Findings

Enhanced Babbitt's decomposition theorem

Applications to difference algebraic groups

Solutions to compatibility problems

Abstract

We introduce a class of strongly \'{e}tale difference algebras, whose role in the study of difference equations is analogous to the role of \'{e}tale algebras in the study of algebraic equations. We deduce an improved version of Babbitt's decomposition theorem and we present applications to difference algebraic groups and the compatibility problem.