On GPW-Flat Acts

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.

کلیدواژه ها:

GPW-flat ، Eventually regular monoid ، Eventually left almost regular monoid