Smoothness and locality for nonunital spectral triples

To deal with technical issues in noncommutative geometry for nonunital algebras, we introduce a useful class of algebras and their modules. These algebras and modules allow us to extend all of the smoothness results for spectral triples to the nonunital case. In addition, we show that smooth spectral triples are closed under the C-infinity functional calculus of self-adjoint elements. In the final section we show that our algebras allow the formulation of Poincare Duality and that the algebras of smooth spectral triples are H-unital.