Abstract
A ring R is a Garcia ring provided that the product of two regular elements is unit-regular. We prove that every regular element in a Garcia ring R is the sum/difference of an idempotent and a unit. Furthermore, we prove that every regular element in a weak Garcia ring is the sum of an idempotent and a one-sided unit. These extend several known theorems on (one-sided) unit-regular rings to wider classes of rings with sum summand property.
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Chen, H., Ashrafi, N. & Abdolyousefi, M.S. Regularity and Related Rings. Mediterr. J. Math. 15, 24 (2018). https://doi.org/10.1007/s00009-018-1068-1
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DOI: https://doi.org/10.1007/s00009-018-1068-1