Quasivarieties Of Completely J^（1）-simple Semigroup

In this thesis, we study completely J(l)-simple semigroups. A semigroup is called a completely J(l)-simple semigroup if it is isomorphic to some Rees matrix semigroup over a left cancellative monoid. This thesis is divided into three chapters.In Chapter1, we introduce some related concepts and list some known results.In Chapter2, we investigate completely J(l)-simple semigroup. It is proved that all completely J(l)-simple semigroups form a quasivariety of algebras. Some characterizations and variety properties of completely J(l)-simple semigroups are obtained.In Chapter3, we investigate free completely K(l)-simple semigroup. The construction of free completely K(l)-simple semigroups is given. It is found that a free completely J(l)-simple semigroup is just a free completely J*-simple semigroup and also a full subsemigroup of some completely simple semigroups.