Exchange Rings Satisfying the n-Stable Range Condition, II

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.

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Correspondence to Huanyin Chen.

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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

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Keywords

  • exchange ring
  • n-stable range condition