S-COTORSION MODULES AND DIMENSIONS

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