hamidieh rashidi

In this article, we present GPW-flatness property of acts over monoids, which is a generalization of principal weak flatness. We say that a right S-act A_S is GPW-flat if for every s ∈ S, there exists a natural number n = n_(s,A_S ) ∈ N such that the functor A_S ⊗ S− preserves the embedding of the principal left ideal S(Ss^n) into SS. We show that a right S-act A_S is GPW-flat if and only if for every s ∈ S there exists a natural number n = n(s,A_S ) ∈ N such that the corresponding ϕ is surjective for the pullback diagram P(Ss^n, Ss^n, ι, ι, S), where ι : S(Ss^n) → SS is a monomorphism of left S-acts. Also we give some general properties and a characterization of monoids for which this condition of their acts implies some other properties and vice versa.