Homological characteristics of operator algebras (Q1819333)

A Banach algebra is called hereditary if every of its closed left ideals is a projective \(A\)-module. For functional algebras \(C(\Omega)\) A. Ya. Khelemski has proved a characterization as algebras with hereditary paracompact spectrum. In the paper under review two results are proved: 1) Separable \(C^*\)-algebras are all hereditary. 2) Infinite dimensional von Neumann algebras are not hereditary.