  This paper shows that Cohen-Macaulay algebras can be algebraically
approximated in such a way that their Cohen-Macaulayness and minimal Betti
numbers are preserved. This is achieved by showing that finitely generated
modules over power series rings can be algebraically approximated in a manner
that preserves their diagrams of initial exponents and their minimal Betti
numbers. These results are also applied to obtain an approximation result for
flat homomorphisms from rings of power series to Cohen-Macaulay algebras.
