On The Structure Of A Class Of Quasi-regular Semigroups

The theory of semigroups is an important branch of algebra. From the system study of semigroups up to now, the study of regular semigroups and their subclasses is always an essential direction in the study of the theory of semigroups. As an important generalization of regular semigroup, quasi-regular semigroups are paied attention to by more and more people since more than half a century.J.L.Galbiati and M.L.Veronesis studied firstly quasi-regular semigroups in 《On quasi- completely regular semigroups》 , and depicted the basic properties and characteristics of quasi-regular semigroups. M.Ciric and S.Bogdanovic studied quasi-regular semigroups ,and extended the structure theorem of orthodox semigroups in the class of regular semigroups to quasi-regular semigroups. In 1996, K.P.Shum and Y.Q.Guo overviewed completely and systematically the main results on quasi-regular semigroups in 《 The regular semigroups and its generalizations 》 .This paper studies mainly a quasi-regular semigroup, so-called quasi-right semigroup, which is a quasi-regular semigroup with left central idempotents and the set of regular elements is an ideal of it. This paper give the basic properties and characteristics of quasi-right semigroups , and construct the algebra structures of a quasi-right semigroup and some of its special cases.The full text is divided into four chapters:In the first chapter, we give some basic notations and some preparations; we give some definitions and properties for quasi-right semigroups in the second chapter; in the third chapter, we build, up the structure of a quasi-right semigroup by using the concept of △-product ; lastly, we introduce the concept of 9- product, and give a structure of a strong quasi-right semigroup.