In:
Algebra Colloquium, World Scientific Pub Co Pte Ltd, Vol. 14, No. 03 ( 2007-09), p. 403-416
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 K 0 -simplicity of such rings in the sense of [3], and investigate the norm completeness of their K 0 -groups. Finally, we characterize the primitive idempotents in R by K 0 (R) with ordered structure, from which we can further determine completely the structure of K 0 (R).
Type of Medium:
Online Resource
ISSN:
1005-3867
,
0219-1733
DOI:
10.1142/S1005386707000375
Language:
English
Publisher:
World Scientific Pub Co Pte Ltd
Publication Date:
2007
detail.hit.zdb_id:
1480585-6
SSG:
17,1
Permalink