Some Studies On Varieties Of Completely Regular Semigroups

Let A be a non-empty set, FA the free semigroup on A and γ the smallest regular band congruence on FA.Then RA=FA/γ is the free regular band on FA.|RA|is the cardinality of RA.In this thesis, we prove that (u, v)∈γ if and only if i(u)=i(v), f(u)=f(v). We also show thatBy using Green’s relations and the method of congruences, we prove that According to some basic properties and results of the operater L, we define y=[(ax)0(ay)0=((ax)0(ay)0)0, axa0(ax)-1(axabaxa)0=(axabaxa)0axa0(xa)-1], and show thatThis thesis consists of three chapters.In Chapter1, we introduce some definitions and lemmas, fix some notation which is used in the remaining part.In Chapter2, a formula to calculate|RA|is given.In Chapter3, we find an identity representation for the variety NB(?)∨(L(?))HA.