Characterizing Subvarieties Of The Variety Of Bands By Forbidden Divisors

On the basis of the characterization of the lattice of proper varieties of bands by Gerhard and Petrich, we firstly characterize subvarieties of the variety of bands by forbidden divisors, and each type contains infinite subvarieties. On this basis, we can characterize the structure of forbidden divisors by a fundamental semilattice of semigroups.This thesis contains three chapters.In Chapter 1, we introduce some definitions and lemmas, fix some notation which is used in the remaining part.In Chapter 2, we obtain the forbidden divisors of [Gn= In] and [Gn= Hn], then we also obtain similarly the forbidden divisors of [Gn= In] and [Gn= Hn], so the forbidden divisors of all subvarieties of the variety of bands are gived.In Chapter 3, We define a mapping, then characterize the structure of forbidden divisors by a fundamental semilattice of semigroups.