Quotient ordered homomorphisms of ordered semigroups

摘要

As a natural generalization of homomorphisms and congruences of semigroup theory without order, we introduce the concepts of QO-homomorphisms and Q-pseudoorders in ordered semigroup theory. First, we obtain properties and three isomorphism theorems for QO-homomorphisms and Q-pseudoorders, then by use them we investigate Rees Q-pseudoorders determined by ideals of ordered semigroups and Q-pseudoorders on ordered Abelian groups, respectively. [References: 4]