Differential Krull dimension in differential polynomial extensions

TL;DR

This paper explores the differential Krull dimension in differential polynomial extensions, establishing a differential analogue of Jaffard's theorem and demonstrating the absence of dimension anomalies in specific classes of differential rings.

Contribution

It introduces a differential analogue of Jaffard's Special Chain Theorem and shows that certain differential polynomial extensions maintain consistent differential Krull dimension.

Findings

Proved a differential analogue of Jaffard's Special Chain Theorem.

Showed that some differential polynomial extensions have no differential Krull dimension anomaly.

Identified classes of differential rings with stable differential Krull dimension.

Abstract

We investigate the differential Krull dimension of differential polynomials over a differential ring. We prove a differential analogue of Jaffard's Special Chain Theorem and show that differential polynomial extensions of certain classes of differential rings have no anomaly of differential Krull dimension.