Finitely presented S-posets

The purpose of this article is to introduce the theory of presentations of S-posets. We constructgeneral presentations for various S-poset constructions related to sub S-posets and Rees quotients. Moreprecisely, given an S-poset A and a sub S-poset B of A, on the one hand, we construct presentations forB and the Rees quotient A=B using a presentation for A, and on the other hand, we derive a presentationfor A from presentations for B and A=B. We also construct a general presentation for the union of twosub S-posets. From our general presentations, we deduce a number of nite presentability results. Finally,we consider the case where a sub S-posets B has a nite complement in an S-posets A. We show that ifS is a nitely generated pomonoid and B is nitely presented, then A is nitely presented. We also showthat if S belongs to a wide class of all nitely presented pomonoids then the converse also holds.

کلیدواژه ها:

S-poset ، down closed sub S-poset ، nitely presented