Galois correspondence theorem for Picard-Vessiot extensions

TL;DR

This paper extends the Galois correspondence theorem for Picard-Vessiot extensions to a broader class of differential fields, enhancing the theoretical framework of differential Galois theory.

Contribution

It generalizes the definition of the differential Galois group and the Galois correspondence theorem beyond real differential fields.

Findings

Generalized Galois correspondence theorem for all Picard-Vessiot extensions.

Extended the definition of the differential Galois group.

Broadened the applicability of differential Galois theory.

Abstract

In this paper, we generalize the definition of the differential Galois group and the Galois correspondence theorem established previously for Picard-Vessiot extensions of real differential fields with real closed field of constants to any Picard-Vessiot extension.