Some Studies For A Class Of Rpp Semigroups

In the study of semigroup, the regular semigroup's research occupies the dominant position. In the recent several dozens years, some kinds of generalized regular semigroup's research forms an important topic in the theory of semigroups. Rpp semigroups is an important generalization of regular semigroup, it's research aroused people's universal attention.About of rpp semigroups, Fountain firstly studied properties and structure of C — rpp semigroup[6], then Y.Q.Guo, K.P.Shum , X.J.Guo studied Left (Right) C — rpp semigroups [7,12,21-25,29,30] , Strongly rpp semigroups and Supper rpp semigroups W, and built up their structure. Those research results provided basis for the overall construction research of rpp semigroups.By the definition of Green(e)-relation and the analogue of generalized Green's lemma, this paper first studied some properties of H(e)-class, D(e)--class of rpp semigroups, then by left (right) S-system , (S, T)-bisystem and tensor product, we described a blocked Rees matrix semigroup. Especially, the paper studied primitive rpp semigroups . Lastly , from a primitive rpp semigroup with zero , we built up a type A blocked Rees matrix semigroup and showed a semigroup S is a primitive rpp semigroup if and only if S is isomorphic toa type A blocked Rees matrix semigroup.