IBN Rings and Orderings on Grothendieck Groups

作     者：Tong Wenting Department of Mathematics Nanjing University Nanjing,210008 China 

作者机构：Department of Mathematics Nanjing University Nanjing China 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：1994年第10卷第3期

页      面：225-230页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：Supported by National Nature Science Foundation of China 

主　　题：IBN Rings and Orderings on Grothendieck Groups Math PSF 

摘      要：Let R be a ring with an identity element.R∈IBN means that Rm■Rn implies m=n,R ∈IBN1 means that Rm ■Rn⊕K implies m≥n,and R ∈IBN2 means that Rm■Rm⊕K implies K=*** this paper we give some characteristic properties of IBN1 and IBN2,with orderings o the Grothendieck *** addition,we obtain the following results:（1）If R ∈IBM1 and all finitely generated projective left R-modules are stably free,then the Grothendieck group Ko（R）is a totally ordered abelian group.（2）If the pre-ordering of the Grothendieck group Ko（R）of a ring R is a partial ordering,then R ∈IBM1 or Ko（R）=0.