Abstract
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.
Acknowledgment
The author would like to thank the referee for his valuable suggestions.