Characterization of idempotent elements in a variant of the finite full transformation semigroup

Abstract

In this research work, we consider a finite set X with n elements and introduce a systematic discussion of the transformation semigroup on the finite set  (namely the full transformation semigroup Tn ) with the aim of studying the variants of this semigroup. There have been many approaches in studying  the variant semigroup (i.e T^α_n for ? ∈ T_n ), especially characterizing of Green’s relation and classification of certain Subsemigroups. In this particular  work we study and characterize the idempotent elements in a variant of the finite full transformation semigroupTn , and present the findings in the form  of results.