On The Study Of(Ordered) R-torsion Free(Ordered) S-acts

In categories of Rees factor acts,cyclic acts and all acts,this paper investigate the characterization of monoids over which R-torsion free property separately im-plies conditions(PF?),(PF??),GP-(P),and GP-flat properties.This paper also give the characterization of R-torsion S-posets,and study the homological classification problems of R-torsion free S-posets.