Let be a ring, a multiplicative subset of . An -module is said to be --flat (- always abbreviates uniformly) if $\Tor^R_1 (M, N)$ is --torsion -module for all -modules . In this paper, we introduce and study the concept of -cotorsion module which is in some way a generalization of the notion of cotorsion module. An -module is said to be -cotorsion if $\Ext^1_R(F,M)=0$ for any --flat module . This new class of modules will be used to characterize --von Neumann regular rings. Hence, we introduce the -cotorsion dimensions of modules and rings. The relations between the introduced dimensions and other (calssical) homological dimensions are discussed. As applications, we give a new upper bound on the global dimension of rings.