Natural Partial Orders And Super Rpp Semigroups

In this thesis, we study natural partial orders on strongly rpp semigroupsand a class of super rpp semigroups, so-called cryptic rpp semigroups, whichare generalizations of cryptic groups. In addition, we investigate a kind ofrpp semigroups whose idempotents can not be compared each other, namedprimitively decomposable rpp semigroups, which are generalizations of com-pletely0-simple semigroups in the range of rpp semigroups. The thesis isdivided into four chapters.In chapter1, we introduce some related knowledge and list some knownresults.In chapter2, we investigate some natural partial orders on a stronglyrpp semigroup, namely the natural partial orders≤sl,≤srand≤s. Then wegive some characterization theorems for the strongly rpp semigroups endowedwith the above natural partial orders. In particular, we determine when asuper rpp semigroup be compatible with the natural partial order≤sl.In chapter3, we consider a sepical kind of cryptic rpp semigroups callednormal cryptic rpp semigroups. By using the natural partial orders defined onstrongly rpp semigroups in chapter2, we obtain some important properties ofpartial orders on super rpp semigroups. Finally, we characterize the normalcryptic rpp semigroups by this natural partial orders.In chapter4, we study primitively decomposable rpp semigroups andget some characterizations for this kind of semigroups. In particular, weestablish the construction theorem.