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Rings of Idempotent Stable Range One |
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| Authors: | Zhou Wang Jianlong Chen Dinesh Khurana Tsit-Yuen Lam |
| Affiliation: | 1. Department of Mathematics, Southeast University, Nanjing, 210096, People??s Republic of China 2. Faculty of Mathematics, Indian Inst.?of Sci.?Edu.?& Res., Mohali, MGSIPA Transit Campus, Sector 26, Chandigarh, 160 019, India 3. Department of Mathematics, University of California, Berkeley, CA, 94720, USA |
| Abstract: | We show that in a ring of stable range 1, any (von Neumann) regular element is clean. Our main results also imply that any unit-regular ring has idempotent stable range 1 (and is therefore clean), and that a semilocal ring has idempotent stable range 1 if and only if it is semiperfect. |
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