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.
