  Differential Graded Algebras can be studied through their Differential Graded
modules. Among these, the compact ones attract particular attention.
  This paper proves that over a suitable chain Differential Graded Algebra R,
each compact Differential Graded module M satisfies amp M >= amp R, where amp
denotes amplitude which is defined in a straightforward way in terms of the
homology of a DG module.
  In other words, the homology of each compact DG module M is at least as long
as the homology of R itself. Conversely, DG modules with shorter homology than
R are not compact, and so in general, there exist DG modules with finitely
generated homology which are not compact.
  Hence, in contrast to ring theory, it makes no sense to define finite global
dimension of DGAs by the condition that each DG module with finitely generated
homology must be compact.
