Exchange rings having ideal-stable range one |
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| Authors: | CHEN Huanyin Li Fu'an |
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| Affiliation: | 1. Department of Mathematics, Hunan Normal University, Changsha 410006, China
2. Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, China |
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| Abstract: | In this paper, we introduce the notion of the ideal-stable range one condition for exchange rings. Some characterizations for this condition are given. Moreover, we show that, for an exchange ringR, ifI is an ideal ofR andR hasI-stable range one, then every regular square matrix overI is the product of an idempotent matrix and an invertible matrix overR, and admits a diagonal reduction. |
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| Keywords: | exchange ring stable range condition diagonal reduction |
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