<正>半群的半直积与圈积是构造和研究半群的重要方法之一。目前对一般半群 (不带序的半群 )的半直积及圈积的研究已有许多结论 ,但是对序半群半直积与圈积的研究很少。I -正则半群和I -逆正则半群是正则半群和逆正则半群在序半群中的推广 ,它们是两类重要的序半群。笔者引入了序半群的半直积的概念 ,给出了两个序半群的半直积是I -正则和I -逆正则半群的充要条件 ,将其应用到圈积中 ,得到圈积是I -正则和I-逆正则半群的充要条件

It is an important method to construct and study semigroups by the semidirect product and wreath product of two semigroups.At present,there are many reports in the semidirect product and wreath product of semigroups(without ordered relation),but there are few references in the semidirect product and wreath product of ordered semigroups.I-regular and I-inverse semigroups are two important classes ordered semigroups as a generalization of regular and inverse semigroups.In this paper,the semidirect product of two pomonoids are introduced,and necessary and sufficient condition are determined for the semidirect product of two ordered monoids to be I-regular and I-inverse semigroup,as an application in wreath product,main theorems in reference \ and \ are obtained.