  For a module-finite algebra over a commutative noetherian ring, we give a
complete description of flat cotorsion modules in terms of prime ideals of the
algebra, as a generalization of Enochs' result for a commutative noetherian
ring. As a consequence, we show that pointwise Matlis duality gives a bijective
correspondence between the isoclasses of indecomposable injective left modules
and the isoclasses of indecomposable flat cotorsion right modules. This
correspondence is an explicit realization of Herzog's homeomorphism induced
from elementary duality of Ziegler spectra.
