Further Results on K0-Groups with Ordered Structure

• 来源期刊: 代数集刊(英文版)
• 关键词: Ko-group generalized abelian exchange ring stable range 1 (e)-group Ko-simplicity Boolean algebra norm completeness
• 年，卷（期）: 2007,（3）
• 页码范围: 403-416
• 页数: 14页
• 语种: 英文

摘要

This paper is a continuation of our previous work [10]. By GAERS-1,we denote the class of generalized abelian exchange rings with stable range 1.In this paper,we first prove that for any ring R (E) GAERS-1 and any ideal I of R,Ko(R/I)is an archimedean (e)-group,which is a natural generalization of [10,Theorem 5.3].As applications,we establish explicit characterizations for the Ko-simplicity of such rings in the sense of [3],and investigate the norm completeness of their Ko-groups.Finally,we characterize the primitive idempotents in R by Ko(R) with ordered structure,from which we can further determine completely the structure of Ko(R).