Let (R, [mfr ]) be a local Noetherian ring. We show
that if R is complete, then an R-module M satisfies local
duality if and only if the Bass numbers μi([mfr ],
M) are finite for all i. The class of modules with finite Bass
numbers includes all finitely generated, all Artinian, and all Matlis
reflexive R-modules. If the ring R is not
complete, we show by example that modules with finite Bass numbers need not
satisfy local duality. We
prove that Matlis reflexive modules satisfy local duality in general, where
R is any local ring with a
dualizing complex.