On K₂ Group Of General Ring With Stable Range 1

This paper is focused on K2-group of a general ring with stable rang 1,and divided into five chapters.In Chapter 1,we introduce briefly the history of algebraic K-theory,the backgrounds of our research and structure of the paper.In Chapter 2,the basic related concepts of the group K0,K1,K2 over a ring R are discussed,and the K2-group of a ring with stable rang lis explicitly described.In Chapter 3,we investigate the properties of Steinberg group St3(R),and focused on the subgroup of group St3(R),called group M3(R).Moreover,generators and some basic properties of group M3(R)are also described.Chapter 4 starts with the group KR over a ring,we discuss the some properties of general Keune symbols.Take group K(R),H3(R),M3(R)as a template in Chapter 3,we will construct group M3(R)denoted by (?)3(R),and give the definition of all generators and properties of group (?)3(R).Some other questions,which need more attention and research in the next step,are illustrated in the part of the summary and prospect of Chapter 5.