Quotient principal factors of an ordered semigroup

In this paper, we introduce the concepts of 0-minimal ideals, 0-simple orde red semigroups, Rees factor ordered semigroups, natural QO-homomorphisms, q uotient principal factors and semisimple ordered semigroups, and discuss ch aracterizations, properties and relationships concerning them. Moreover, we generalize the principal series theory and relative ideal series theory of semigroups (without order) to general ordered semigroups and semisimple or dered semigroups, respectively.