Congruences on Zappa-Szép Products of Semilattices with An Identity and Groups

摘要

Let P =E (8) G be a Zappa-Szép product of a semilattice E with an identity and a group G.In this paper,we first introduce the concept of congruence pairs for P,and then prove that every congruence on P can be described by such a congruence pair.In fact the congruence lattice on P is lattice-isomorphic to the set of all congruence pairs for P.Finally,we characterize group congruences on P.