Some Studies On Gr(?)bner-Shirshov Bases And Forbidden Subsemigroups Of Bands

The thesis mainly has two parts.In the first part,a Grobner-shirshov basis for a free band is given.In the second part,we describe the band variety with identity X4X2X1X3=X4X2X1X3X4X2X3X2X1X3]in terms of prohibited subsemigroups.This thesis consists of three chapters.In Chapter 1,we introduce some definitions and lemmas,fix some notation which is used in the remaining parts.In Chapter 2,we give the definition of Grobner-shirshov basis and introduce the Composition-Diamond lemma.At the same time,we give a Grobner-shirshov basis of a free band.In Chapter 3,we characterize a band variety in terms of forbidden subsemi-groups.