An invariant for difference field extensions

TL;DR

This paper introduces a new invariant called the distant degree for difference field extensions, explores its properties, and generalizes it to groups with automorphisms, advancing the understanding of difference algebra structures.

Contribution

The paper presents the definition of the distant degree invariant and extends it to automorphism groups, providing new tools for difference algebra analysis.

Findings

Defined the distant degree invariant for difference field extensions

Explored properties of the invariant

Generalized the invariant to groups with automorphisms

Abstract

In this paper we introduce a new invariant (the distant degree) for difference field extensions of finite transcendence degree, and we explore some of its properties. We also discuss a generalisation of this invariant and of the limit degree to groups with an automorphism.