Generalizations Of Clifford Semigroups

The study of regular semigroups is always an important part in the theory of semigroups. The class of Clifford semigroups is an important subclass of the class of regular semigroups. In 1941, Clifford first studied these semigroups and gave a fine structure theorem for Clifford semigroups. Later on, P.Y.Zhu, Y.Q.Guo and K.P.Shum extended Clifford semigroups in the class of regular semigroups and gave the definition of left C-semigroups in 1991. In the same time, the basic characteristics of left C-semigroups were researched and the ζ-product of left C-semigroups was described. In 1995, Y.Q.Guo, X.M.Ren and K.P.Shum also built a new structure of left C-semigroups, that is, △-product. On the other hand, X.M.Ren, Y.Q.Guo and K.P.Shum extended Clifford semigroups to the class of quasiregular semigroups in 1994. They defined Clifford quasiregular semigroups and gave a θ-product structure of this kind of semigroups.In this thesis, the left cross product of left C-semigroups is investigated. It is proved that the left cross product of a left regular band and a Clifford semigroup is the left C-semigroup; Conversely, any left C-semigroup can be constructed by using the left cross product of a left regular band and a Clifford semigroup. And their two special situations are considered. Secondly, we research the congruence on Clifford quasiregular semigroups by using central congruence pairs on Clifford quasiregular semigroups. It is proved that any congruences on Clifford quasiregular semigroups can be unique expressed by central congruence pairs.