S-Pure Projective Modules And S-Pure Flat Modules

Let R be a ring,S a set-presentable class of finitely presented left R-modules containing R. In this article, we study some properties of S-pure projective module and S-pure flat module, and give some characterizations of S-pure flat dimension. In addition, we introduce the concepts of S-cotorsion pair and S-cotorsion module, and give some characterizations of S-pure projective module and S-pure flat module in S-cotorsion pair. Finally, we investigate a special S-pure flat module-C-pure flat module, and study the relationship between C-pure flat module and C-pure projective module, C-pure flat module and RD-pure flat module, C-pure flat module and FC-pure flat module.