  For finitely generated module $M$ over a local ring $R$, the conventional
notions of complete intersection dimension $\cid_R M$ and Cohen-Macaulay
dimension $\cmdim_R M$ do not extend to cover the case of infinitely generated
modules. In this paper we introduce similar invariants for not necessarily
finitely generated modules, (namely, complete intersection flat and
Cohen-Macaulay flat dimensions) which for finitely generated modules, coincide
with the corresponding classical ones.
