Exchange Rings Satisfying the n-Stable Range Condition, Ⅱ

• 来源期刊: 代数集刊（英文版）
• 关键词: exchange ring n-stable range condition
• 年，卷（期）: 2003,（1）
• 页码范围: 1-8
• 页数: 8页
• 语种: 英文

摘要

This is a continuation of the paper [14]. It is shown that any finite subdirect product of exchange rings satisfying the n-stable range condition is still an exchange ring satisfying the n-stable range condition. Furthermore, we give necessary and sufficient conditions on matrices over an exchange ring R, under which R satisfies the n-stable range condition. This generalizes the corresponding results for unit-regular rings and the stable range one condition.