EXTENSIONS OF HILBERT C-MODULES II

Abstract. We describe the pullback construction in the category of Hilbert C-modules (with a suitable class of morphisms) in terms of pullbacks of underlying C-algebras. In the second section the Busby in-variant for extensions of Hilbert C-modules is introduced and it is proved that each extension is uniquely determined, up to isomorphism, by the corresponding Busby map. The induced extensions of the underlying C-algebras as well as of the corresponding linking algebras are also discussed. The paper ends with a Hilbert C-module version of a familiar result which states that a C-algebra is projective if and only if it is corona projective. 1