Some Studies Of Type B Semigroups

This thesis consists of five chapters. In this thesis, we mainly study type B semigroupsby considering their properties and structures, which include proper type B semigroups, goodcongruences on type B semigroups and the construction of the transltional hull of type Bsemigroups.The first chapter illustrates the purposes and meanings of this thesis. Here we providesome basic definitions and known properties of abundant semigroups, which are repeatedlyused in the sequel.We study a class of proper type B semigroups and get some related properties in chaptertwo. Moreover, we introduce the notion of structure mappingsf e,fandy e,fon type Bsemigroups, and obtain the sufficient and necessary conditions for a type B semigroup to beproper.Good congruences on type B semigroups are taken into consideration in chapter three.We prove some relevant conditions that the greatest congruence m on a type B semigroupS contained inH*is a good congruence on S. Further more, we show that S/r is stillto be a type B semigroup for an arbitrary good congruence r on a type B semigroup S.In the fourth chapter, we study the construction of the translational hulls of type Bsemigroups and get some related results.In the last chapter, we generalize the work that we have done, and give some problemsthat we still need to take into account in the future.