Vol. 34, No. 3, 1970

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On the Galois theory of separable algebras

Herbert Frederick Kreimer, Jr.

Vol. 34 (1970), No. 3, 729–740

This note presents a Galois theory for a separable algebra Λ over a semi-local ring R without imposing any restrictions on the presence of idempotent elements in Λ. If suitable restrictions are placed on the existence of idempotent elements in Λ, then such a Galois theory has been obtained by L. N. Childs and F. R. DeMeyer; and the results presented here are extensions of results obtained by Childs and DeMeyer. In more recent work, DeMeyer has extended the Galois theory to algebras over a class of commutative rings more general than semi-local rings. After treating the simpler case of algebras over a semi-local ring, it is indicated in an addendum to this paper how the Galois theory presented here may also be extended to algebras over this more general class of commutative rings.

Mathematical Subject Classification
Primary: 16.70
Received: 29 October 1969
Published: 1 September 1970
Herbert Frederick Kreimer, Jr.