Structures Of Some Band-related Unions Of Groups

A band-related completely regular semigroup is defined by the additional identi-ty ((a~0b~0)~0c~0)~0=(a~0(b~0c~0)~0)~0. On the one hand, we apply a fundamental semilattice of semigroup to giving construction of a band-related completely regular semigroup; on the other hand, we describe structures of some kinds of band-related completely regular semigroups. On the bases, the structure of a normal band is presented from a new perspective.This thesis is divided into four chapters.In Chapter 1, we introduce some definitions and lemmas, fix some notation which is used in the remaining part.In Chapter 2, we give definition of band-related completely regular semigroup and apply a fundamental semilattice of semigroup to constructing it. At the same time, the structures for regular band-related and normal band-related completely regular semigroups are discussed.In Chapter 3, we describe structures of left (right) seminormal orthogroup, and left (right) semiregular orthogroups. On the bases, the structure of a normal band is constructed in a new way.In Chapter 4, structures of left (right) seminormal cryptogroups and left (right) semiregular cryptogroups are discussed.