S-flat cotorsion pair

Let R be a commutative ring, and let S be a multiplicative subset of R. In this paper, we investigate the notion of S-cotorsion modules. An R-module C is called S-cotorsion if Ext^1ₑ (F, C) = 0 for every S-flat R-module F. Among other results, we establish that the pair (SF, SC), where SF denotes the class of all S-flat R-modules and SC denotes the class of all S-cotorsion modules, forms a hereditary perfect cotorsion pair. As applications, we provide characterizations of S-perfect rings in terms of S-cotorsion modules. We conclude the paper with results on SF-preenvelopes. Namely, we prove that if every module has an SF-preenvelope, then R is S-coherent. Furthermore, we establish the converse under the condition that RS is a finitely presented R-module.