On MF-projective modules

In this paper, we study the left orthogonal class of max-flat modules which are homological objects related to s-pure exact sequences and module homomorphisms. Namely, a right $A$ is called MF-projective if ${Ext}^{1}_{R}(A,B)=0$ for any $R$-module $B$, strongly ${Ext}^{i}_{R}(A,B)=0$ all $R$-modules $B$ $i\geq 1$. Firstly, give some properties $MF$-projective SMF-projective modules. Then introduce dimensions rings. The relations between introduced other (classical) discussed. We characterize classes rings such as perfect rings, $QF$ max-hereditary by $(S)MF$-projective also whose ideals MF-projective. Finally, projective.