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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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Wang, Z., Chen, J., Khurana, D. et al. Rings of Idempotent Stable Range One. Algebr Represent Theor 15, 195–200 (2012). https://doi.org/10.1007/s10468-011-9276-4
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DOI: https://doi.org/10.1007/s10468-011-9276-4