On S-torsion exact sequences and Si-projective modules (i=1,2).

Let R be a commutative ring and S a given multiplicative closed subset of R. In this paper, we introduce the new concept of S -torsion exact sequences (respectively, S -torsion commutative diagrams) as a generalization of exact sequences (respectively, commutative diagrams). As an application, they can be used to characterize two classes of modules that are generalizations of projective modules. [ABSTRACT FROM AUTHOR]