Rds Type Lie Algebra

Study the construction and the classification of the Lie Algebra is one of the basic work of the algebra. Especially to the finite dimensional Lie Algebra is a very important work.RDS-type Lie Algebra is a special class of Lie Algebra. We define it through study its ideal lattice.This class of Lie Algebra is more than semisimple Lie Algebra. So study the construction and the classification of it can help us to study the whole Lie Algebra.The main work of this paper is to study the RDS-type Lie Algebra. In this paper we study its basic properties and decided the construction of the RDS-type Lie Algebra those dimensional is lower or equal to 4. The most important work of this paper is that we give a classification of the RDS-type Lie Algebra those dimensional is equal to 4.In the first chapter we define the n-RDS-type Lie Algebra and give its main properties and some theorems about it. The main theorem is theorem 1.1. This theorem decided all n-RDS-type Lie Algebra (n>2).In the second chapter we give a necessary and sufficient conditions of the definition of the RDS-type Lie Algebra; then we illustrate and proof some basic lemma about the RDS-type Lie Algebra.The third chapter is the main part of this paper. First we class 1-3 dimensional RDS-type Lie Algebra, then we decided all 4 dimensional RDS-type Lie Algebra..