Some Studies For Right C-rpp Semigroups

From the system research of semigroups up to now,the investigation of regular semigroupsand their subclasses is always a critical direction in the theory of semigroups.Inthe recent years,many authors generalized regular semigroups in different ways.Hence,the studies for generalized regular semigroups becomes an important research topic.A semigroup S is called an rpp semigroup,if every L^*- class of S contains at least oneidempotent.An rpp semigroup is called a right C-rpp semigroup,if D^e is a congruenceon S and Se(?)eS for all e∈E,where D^e=L^*∨R.In this paper,we mainly discuss the construction for right C-rpp semigroups whoseidempotents form a right regular band.In particular,we establish the constructionfor right C-rpp semigroups by right cross products.This paper proves that if M=[Y；M_α,(?)_α,β]is a strong semilattice of left cancellative monoids M_α,Λ=∪_α∈YΛ_αis right regular band.Then,a right cross product M (?)_θΛof M andΛis a right C-rpp semigroup.Conversely,any right C-rpp semigroups can be constructed in this way.