An intrinsic characterization of Picard-Vessiot extensions

TL;DR

This paper provides a new intrinsic characterization of Picard-Vessiot extensions in differential Galois theory, paralleling classical Galois field extension characterizations.

Contribution

It introduces an intrinsic, field-theoretic characterization of Picard-Vessiot extensions, bridging differential and classical Galois theories.

Findings

Provides a new characterization of Picard-Vessiot extensions

Establishes analogy with classical Galois field extensions

Enhances understanding of differential Galois theory

Abstract

We present a characterization of differential Picard-Vessiot extensions which is analogous to the field theoretic characterization of Galois extensions in classical Galois theory.