Several Studies On E-Inverse Semigroups And E-Semigroups

This master dissertation consists of four chapters.In this paper,the concepts of E-inverse semigroups and E-semigroups are introduced.We investigate the properties, constructions and congruences of E-inverse semigroups and E- semigroups. especially,E-inverse semigroups.And some new results on characterization of E-inverse semigroups are studied.The first part is a brief introduction,basic knowledge is introduced.We show the research background,research ways and research contents of the paper.In chapterâ…¡,the rectangular group congruence on the E-inverse semigroup S is first described by means of the rectangular group congruence pairs.Furthermore, we can obtain a isomorphism between the rectangular group congruences and the rectangular group congruence pairs.In the end,The basic properties of E-inverse semigroups are studied and some useful properties are known.In chapterâ…¢,we study its various ideals of E-inverse semigroups,particularly, concerning all the kind of ideals.Finally,we give some particular properties of ideals on E-inverse semigroups.Chapterâ…£is devoted to investigate some new results on a characterization of E-semigroups by means of one new definitions of sandwich set.By the approach, we can get many new equivalent conditions which contribute to know the structure of sandwich set.