中文摘要：

首先引入了序半群定向完备化的概念;其次证明了序半群的序理想之集和理想之集都是连续定向完备序半群,进而序半群的序理想之集和负序半群的理想之集是它们的定向完备化;最后得到了序半群范畴的几个满子范畴的反射子范畴。

英文摘要：

Firstly, the concept of directed-completion of ordered semigroup is given. Secondly, it is proved that for every ordered semigroup, the set of all its ordered ideals and the set of all its ideals are both continuous directed-complete ordered semigroups. Moreover, the set of all the ordered ideals is a directed-completion for every ordered semigroup and the set of all the ideals is a directed-completion for every negative ordered semigroup.Finally,the reflective relationship among some full subcategories of the category of ordered semigroups is obtained.