Principal homogeneous spaces and Galois extensions

Andy R. Magid

Vol. 53 (1974), No. 2, 501–513

DOI: 10.2140/pjm.1974.53.501

Abstract

Principal homogeneous spaces for finite groups in the category of sets with groupoid action are studied and classified. The results are applied to separable algebras, using the fundamental theorem of Galois theory of commutative rings, which embeds the category of separable algebras into the category of sets on which a certain profinite groupoid acts.

Mathematical Subject Classification 2000

Primary: 13B05

Milestones

Received: 12 March 1973

Revised: 28 November 1973

Published: 1 August 1974