On GPW-Flat Acts

Abstract

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 in S, there exists a natural number n = n_ {(s, A_{S})} in mathbb{N} such that the functor A_{S} otimes {}_{S}- preserves the embedding of the principal left ideal {}_{S}(Ss^n) into {}_{S}S. We show that a right S-act A_{S} is GPW-flat if and only if for every s in S there exists a natural number n = n_{(s, A_{S})} in mathbb{N} such that the corresponding varphi is surjective for the pullback diagram P(Ss^n, Ss^n, iota, iota, S), where iota : {}_{S}(Ss^n) rightarrow {}_{S}S 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.