Abstract
Let R be a unital semi-simple commutative complex Banach algebra, and let M ( R ) denote its maximal ideal space, equipped with the Gelfand topology. Sufficient topological conditions are given on M ( R ) for R to be a projective free ring, that is, a ring in which every finitely generated projective R-module is free. Several examples are included, notably the Hardy algebra H ∞ ( X ) of bounded holomorphic functions on a Riemann surface of finite type, and also some algebras of stable transfer functions arising in control theory.
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