Distributivity Of Proper Subvariety Lattice Of The Band Variety And Green’s Relation Minorization For Idempotents On Unions Of Groups

In the thesis, we prove that the proper subvariety lattice of the band variety is dis-tributive, and give equivalent conditions of Green’s relation minorizations for idempotents on completely regular semigroups (also called unions of groups).The thesis consists of three chapters.In the first chapter, we introduce some definitions and lemmas of semigroups and completely regular semigroups, and also fix some notation which is used in the remaining part.In the second chapter, we prove that the proper subvariety lattice of the band variety is a distributive lattice.In the third chapter, we discuss equivalent conditions of Green’s relation minoriza-tions for idempotents on completely regular semigroups. Moreover, some simple results on the relationship between minorization and majorization of Green’s relations on completely regular semigroups are obtained.