This is a continuation of the paper . 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.
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2000 Mathematics Subject Classification: 19B10, 16E50
This work was supported by the National Natural Science Foundation of China (Grant No. 19801012) and the Ministry of Education of China.
Communicated by Weimin Xue
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Chen, H., Li, Fa. Exchange Rings Satisfying the n-Stable Range Condition, II. Algebra Colloq. 10, 1–8 (2003). https://doi.org/10.1007/s100110300000
- exchange ring
- n-stable range condition