Separable algebras over a commutative Banach algebra

Ian George Craw and Susan Ross

Vol. 104 (1983), No. 2, 317–336

DOI: 10.2140/pjm.1983.104.317

Abstract

We show that the projective separable algebras over a commutative Banach algebra R with maximal ideal space X are the same as those over C(X). Two consequences of this are the identification of the Brauer group of R with that of C(X), and the identification of the set of covering algebras of R with the finitely fibred covering spaces of X.

Mathematical Subject Classification 2000

Primary: 46J99

Secondary: 46H99, 46M99

Milestones

Received: 29 March 1981

Published: 1 February 1983