A CHARACTERIZATION OF S1-PROJECTIVE MODULES

Recently, Zhao, Pu, Chen, and Xiao introduced and investigated novel concepts regarding S-torsion exact sequences, S-torsion commutative diagrams, and Si-projective modules (for i = 1, 2) in the context of a commutative ring R and a multiplicative subset S of R. Their research included various results, such as proving that an R-module is S1-projective if it is S-torsion isomorphic to a projective module. In this paper, we further examine properties of S-torsion exact sequences and S-torsion commutative diagrams, and we establish the equivalence between an R-module being S1-projective and its S-torsion isomorphism to a projective module.