Some Studies For Super (?)-unipotent Semigroups And Right-e Wlpp Semigroups

The algebra theory of semigroups, driven by computer science and information science, has been developed into a branch of algebra for several years. From the systematic research of semigroups up to now, the research of regular semigroups and their subclasses have been the main direction in the theory of semigroups. In recently years, many authors have ob-tained kinds of regular semigroups and their subclasses by generalized Green's relations from different angles. In this thesis, we mainly introduce the properties and the semilattice de-composition of super R-unipotent Semigroups, right-e wlpp semigroups. It can be divided into the following chapters.We first introduce the definition and properties of semigroups, such as the definition of regular band and *-ideal, isomorphism, spined product, congruence relations and so on.In the second chapter of this thesis, we prove the properties, some characterizations and the structure theorem of super R-unipotent semigroups(i.e.,left C-a semigroups). Then we introduce the definition of J-primitive U-abundant semigroups and U-admissible left (right) ideals. And later on, we obtain some characterizations of super R-unipotent semigroups.In the last part of this paper, we give the definition of right-e wlpp semigroups and provide a new structure theorem of right-e wlpp semigroups. A wlpp semigroup S is right-e wlpp semigroup if xey=xye for all x,y∈S1 and x≠1. This kind of semigroups is a spined product of C-wlpp semigroup and left normal band with respect to a semilattice Y. We also prove right-e wlpp semigroup is strong semilattice of L-right cancellative planks.