The L-ordered semigroups based on L-partial orders

Abstract Fuzzy (frame-valued) ordered semigroups are investigated with the orders being L -partial orders. In this framework, L -left (resp. L -right) ideals, L -bi-ideals and L -quasi-ideals of an L -ordered semigroup are discussed, the idea of which is applied to the characterizations of regular and duo L -ordered semigroups. In addition, the relationship between an L -ordered semigroup and an L -topological semigroup is studied. As a consequence, an isomorphism between the category of L -ordered semigroups and the category of L -topological semigroups with the topologies being L - T 0 and Alexandrov is obtained.