Some Studies For Generalized Regular Semigroups

The theory of semigroups is an important branch of algebra.From the system research of semigroups up to now,the investigation of regular semigroups and their subclasses is always an critical direction in the theory of semigroups.With the development of semigroup theory,many authors generalized regular semigroups in different ways.In this paper,we mainly study two kinds of generalized regular semigroups.In the first part of the thesis,we discuss L*-inverse semigroups and its subclass U*-inverse semigroups.Ren Xueming and K.P.Shum in[7]introduced the concept of L*inverse semigroups and established the construction for L*-inverse semigroups.Now,on the basis of their work we describe the minimum cancellative monoid congruence on a L*-inverse semigroup,and give the definition of U*-inverse semigroups.Furthermore,we also depicte the basic properties and characteristics of such semigroups.In the second part,we do some work on quasi-inverse semigroups.We firstly introduce the concept of quasi-inverse semigroups.Then,we discuss basic properties and characteristics of the least group congruence on quasi-regular semigroups.Lastly,we give group congruences and the smallest group congruence of quasi-inverse semigroups.