Vol. 33, No. 3, 1970

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Locally Galois algebras

Andy R. Magid

Vol. 33 (1970), No. 3, 707–724

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
Received: 11 August 1969
Published: 1 June 1970
Andy R. Magid
Department of Mathematics
University of Oklahoma
601 Elm Avenue
PHSC 423
Norman OK 73019-0315
United States