Some Characterizations Based On Type B Semigroup Structures

This paper consists of five chapters.In this paper,we mainly study the structure theorems of proper type B semigroup and a ~*-prehomomorphism of a type B semigroup.The first chapter mainly introduces the research purpose and significance of this thesis and explains the research status of type B semigroups at home and abroad.Especially,some the basic concepts of semigroups are given.In the second chapter,we first introduce the notion of a left admissible triple.A characterization of left type B semigroup is given.Furthermore,we establish the structure of a proper type B,and obtain some results.A ~*-prehomomorphism of a type B semigroups is considered in chapter three.After obtaining some basic properties,we get some structure theorems and give some conditions for a type B semigroup which is constructed by using the ~*-prehomomorphism to be proper.In the fourth chapter,we introduce the notion of E-unitary good cover for an abundant semigroup,and prove that every type B semigroups with compatible natural partial order admits an E-unitary good cover.In the last chapter,we review the previous work and proposes some suggestions which can be studied in the future.