a new characterization of absolutely po-pure and absolutely pure s-posets

In this paper, we investigate po-purity using finitely presented s-posets, and give some equivalent conditions under which an s-poset is absolutely po-pure. we also introduce strongly finitely presented s-posets to characterize absolutely pure s-posets. similar to the acts, every finitely presented cyclic s-posets is isomorphic to a factor s-poset of a pomonoid s by a finitely generated right congruence on s. finally, the relationships between regular injectivity and absolute po-purity are considered.