The Operator L On The Lattice Of Proper Subvarieties Of The Variety Of Bands

This thesis discusses the operator L on the lattice of subvarieties of the variety of bands. Let Hn, Hn, Jn and Jn be subvarieties of the variety of bands, L be the local operator on the lattice of varieties of completely regular semigroups. We investigate the operator L on the lattice of subvarieties of the band variety. It is proved that L Hn=Hn,LHn=Hn,LJn=Hn+1, LJn=Hn+1and the operator L is a V-homomorphism on the lattice of subvarieties of the variety of bands.The thesis consists of three chapters.In the first chapter, we introduce some definitions and lemmas about semigroup, band, lattice, variety and the local operator, fix some notations which used usually later.In the second chapter, we discuss the Operator L on the lattice of subvarieties of the variety of bandsLastly, we prove that the operator L is a V-homomorphism on the lattice of subva-rieties of the variety of bands.