Some Studies On A Class Of Transformation Semigroups

Let F_M denote the full transformation semigroup on a finite set M, where A is a nonempty subset of M,Obviously,F_M is a subsemigroup of F_M.And it is easy to see that if A = M, then F_M = J_M.In this thesis, we mainly investigate some equivalence relations on the transformation semigroup F_M,and determine some classes of F_M. This dissertation consists of three chapters in all.Firstly, some basis concepts on semigroup are proposed. Then, we introduce the Green relations,*-Green relations and some special classes of semigroup. Secondly, we focus our attention on F_M.After showing the Green relations of F_M,we describe the regular elements and completely regular elements of F_M.And, we determine the regularity and completely regularity of F_M.Lastly, we give the *-Green relations and ensure the abundance of F_M.So,the supper-abundance of F_M is clearly by means of its regularity. In addition, from the above discussion, we provide here an example of abundant semigroup which is not regular.