Locally Galois algebras

Andy R. Magid

Vol. 33 (1970), No. 3, 707–724

DOI: 10.2140/pjm.1970.33.707

Abstract

Separable subalgebras of commutative algebras which (a) are the direct limit of separable subalgebras and (b) have sufficiently many automorphisms are shown to be the fixed rings of groups of automorphisms of the algebra. Necessary and sufficient conditions for an arbitrary subalgebra to be the fixed ring of a group are examined.

Also, we show that every element of every separable algebra over a ring is separable if and only if the ring is von Neumann regular.

Mathematical Subject Classification

Primary: 13.70

Milestones

Received: 11 August 1969

Published: 1 June 1970