Partial generalized crossed products and a seven-term exact sequence

TL;DR

This paper generalizes the Chase-Harrison-Rosenberg sequence to partial Galois extensions of commutative rings, providing a seven-term exact sequence that broadens the understanding of such algebraic structures.

Contribution

It introduces a new seven-term exact sequence for partial Galois extensions, extending classical results to a more general setting.

Findings

Established a seven-term exact sequence for partial Galois extensions

Generalized classical Galois theory results to partial contexts

Enhanced understanding of algebraic structures in commutative rings

Abstract

For a partial Galois extension of commutative rings we give a seven term exact sequence which generalize the Chase-Harrison-Rosenberg sequence.