CSF S-posets And C(P) S-posets

Let S be a pomonoid.This paper mainly introduce the generalizations of I-regular acts in the category of S-posets,we called them CSF S-posets and C(P)S-posets.In this paper we discuss some properties of CSF S-posets and C(P)S-posets,as applications,left semicancellable order monoid,right PSF order monoid,left quasi order monoid and right P(P)order monoid are characterized and some results on CSF S-posets and C(P)S-posets can be also obtained.Finally,the properties and the homological classification problems of CSF S-posets and C(P)S-posets of their right Rees factor acts are investigated.