N-the Rds Type Lie Algebras And N-rds Algebraic Groups

n-RDS type Lie Algebra is a special class of Lie Algebra.We define it through the study of the lattice of its ideals.And the discussion of the construction and classification of it can help us to study the whole Lie Algebra.There are particular relations between the closed connected normal subgroups of algebraic groups and the ideals of Lie Algebras.By studying the lattice of the closed connected normal subgroups of algebraic groups,in this thesis a special class of algebraic groups,called n-RDS type algebraic groups,is defined.In this thesis,firstly we introduce the definition and some relative exeamples,and some main properties and theorem and relations between Lie algebra and algebraic group.On this basis,the definition of n-RDS type algebraic groups is gotten.Then,the definition of equivalence conditions is proved.However,it is not easy to study algebraic group.The Lie algebra of algebraic group reflects many of the properties of algebraic group.So in the stduy of n-RDS type algebraic groups,many results are obtained maily by investigation of its Lie algebra,and some properties of the algebraic group are given. Finally,several examples of n-RDS type algebraic groups are given,reflecting the relations between it and n-RDS type Lie algebra.