Subpullbacks and Flatness Properties of S-Posets

In [5 Laan , V. ( 2001 ). Pullbacks and flatness proprties of acts I . Comm. Algebra. 29 ( 2 ): 829 – 850 .[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar], pp. 829–850] study was initiated of flatness properties of right acts A _S over a monoid S that can be described in terms when the functor A _S ?-preserves pullbacks. In that article, familiar flatness properties emerged in a new light, and new properties such as (PWP) and (WP) were discovered. In this article, we extend these results to S-posets. Also we introduce Conditions (WP) _w and (PWP) _w and consider the relation between them and Conditions (WP), (PWP), and po-flatness.