Some Studies On Semigroups Of Transformations That Preserve Equivalence

Let X be a nonempty set,E an equivalence relation on X and T(X)the full transformation semigroup on X.Denote Evidently,TE(X)and TE*(X)are subsemigroups of T(X).The main content researched in this thesis is the algebraic properties of the above two kinds of semigroups of transformations which preserve an equivalence.The equality and compatibility of Green relations,Green*-relations and Green～-relations and some associated subsemigroups of the above two kinds of transformation semigroups are studied.The sufficient or necessary conditions under which these two classes of semigroups and some of their subsemigroups are left regular(right regular,completely regular,intra-regular,orthodox)are given.F-abundant,G-abundant,left magnifying and right magnifying elements in the latter kind of semigroups are characterized.The results enrich and extend the relevant conclusions and contents in the existing literatures.