1. Further Results on K0-Groups with Ordered Structure.
- Author
-
Xinmin Lu and Hourong Qin
- Subjects
RING theory ,ALGEBRAIC fields ,MATHEMATICAL analysis ,GROUP rings ,ALGEBRA ,MATHEMATICS - Abstract
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 ∈ GAERS-1 and any ideal I of R, K
0 (R/I) is an archimedean ℓ-group, which is a natural generalization of [10, Theorem 5.3]. As applications, we establish explicit characterizations for the K0 -simplicity of such rings in the sense of [3], and investigate the norm completeness of their K0 -groups. Finally, we characterize the primitive idempotents in R by K0 (R) with ordered structure, from which we can further determine completely the structure of K0 (R). [ABSTRACT FROM AUTHOR]- Published
- 2007
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