Partial Galois cohomology and related homomorphisms (expanded version)

TL;DR

This paper introduces a seven-term sequence for partial Galois extensions of commutative rings, extending the classical Chase-Harrison-Rosenberg sequence to a broader context.

Contribution

It develops a new seven-term sequence for partial Galois extensions, providing a significant generalization of existing Galois cohomology tools.

Findings

Established a seven-term sequence analogous to Chase-Harrison-Rosenberg

Extended Galois cohomology concepts to partial extensions

Provided new homomorphisms related to partial Galois structures

Abstract

For a partial Galois extension of commutative rings we give a seven terms sequence, which is an analogue of the Chase-Harrison-Rosenberg sequence.