Halimeh Moghbeli

The aim of this paper is to study dcpo-congruences on a S-dcpo; dcpos equipped with a compatible right action of a dcpo-monoid S. In order to characterize S-dcpo congruences, we introduce the concept of a pre-congruence relation, and characterize S-dcpo congruences as equivalence relations generated by pre-congruences. Moreover, applying the notion of \directed kernel" for order-preserving maps, we give a characterization of pre-congruences as directed kernels of surjective S-dcpo maps (Theorem 3.6). Finally, we prove the Decomposition and Isomorphism Theorems for S-dcpo maps.