  We prove a noncompact Serre-Swan theorem characterising modules which are
sections of vector bundles not necessarily trivial at infinity. We then
identify the endomorphism algebras of the resulting modules. The endomorphism
results continue to hold for the generalisation of these modules to
noncommutative, nonunital algebras. Finally, we apply these results to not
necessarily compact noncommutative spin manifolds, proving that Poincare
Duality implies the Morita equivalence of the `algebra of functions' and the
`Clifford algebra.'
