Geodesic
Exchange rings in which all regular elements are one-sided unit-regular
Czechoslovak Mathematical Journal, Tome 58 (2008) no. 4, pp. 899-910.

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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.
Classification : 16D70, 16E20, 16E50, 16U60, 16U99
Keywords: exchange ring; one-sided unit-regularity; idempotent 
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     title = {Exchange rings in which all regular elements are one-sided unit-regular},
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Chen, Huanyin. Exchange rings in which all regular elements are one-sided unit-regular. Czechoslovak Mathematical Journal, Tome 58 (2008) no. 4, pp. 899-910. http://geodesic.mathdoc.fr/item/CMJ_2008__58_4_a2/