Purity in the category of S-posets

Abstract

In this paper, purity of S-posets over a pomonoid S is investigated.We rst study
some basic properties of absolutely po-pure S-posets. Among other results,
it is proved that every regular injective S-poset is absolutely po-pure, and
every absolutely po-pure inequationally compact S-poset is regular injective.
Then, using the notion of semi-nitely presented S-poset based on the nitely
induced S-poset congruence,we nd an equivalent condition for an S-poset to
be 1-po-pure in a regular extension. Finally, a characterization of an absolutely
1-po-pure S-poset is presented.