(1) Department of Mathematics, Zhejiang Normal University Jinhua, Zhejiang, 321004, China;(2) Institute of Mathematics, Academy of Mathematics and System Sciences Chinese Academy of Sciences, Beijing, 100080, China
Abstract:
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.2000 Mathematics Subject Classification: 19B10, 16E50This work was supported by the National Natural Science Foundation of China (Grant No. 19801012) and the Ministry of Education of China.
