Vol. 23, No. 1, 1967

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On automorphisms of separable algebras

Lindsay Nathan Childs and Frank Rimi DeMeyer

Vol. 23 (1967), No. 1, 25–34

This paper presents a Galois theory for separable algebras over a (not necessarily Noetherian) semi-local ring. Our theory is patterned after, but independent of the Galois theory of G. Hochschild; over a perfect field Hochschild’s theory and ours coincide.

In order to present this theory we first present some results concerning separable algebras over semilocal rings. The most important of these is a generalization of the SkolemNoether theorem. Our theorem states that any algebra monomorphism of a separable subalgebra without central idempotents into a central separable algebra whose center is semilocal extends to an inner automorphism.

Mathematical Subject Classification
Primary: 16.70
Secondary: 13.00
Received: 15 March 1966
Revised: 13 October 1966
Published: 1 October 1967
Lindsay Nathan Childs
Frank Rimi DeMeyer