Exchange rings in which all regular elements are one-sided unit-regular
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Let R be an exchange ring in which all regular elements are one-sided unit-regular. Then every regular element in R is the sum of an idempotent and a one-sided unit. Furthermore, we extend this result to exchange rings satisfying related comparability.
Keywordsexchange ring one-sided unit-regularity idempotent
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- W. K. Nicholson and Y. Zhou: Clean rings: A survey, Advances in Ring Theory. Proceedings of the 4th China-Japan-Korea International Conference, 2004, pp. 181–198.Google Scholar