Homological flat dimensions

For finitely generated module $M$ over a local ring $R$, the conventional notions of complete intersection dimension ${\text{cid}}_{R}M$ and Cohen-Macaulay dimension ${\text{cmdim}}_{R}M$ 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.