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Regularity and Related Rings |
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| Authors: | Huanyin?Chen Nahid?Ashrafi |
| Institution: | 1.Department of Mathematics,Hangzhou Normal University,Hangzhou,China;2.Faculty of Mathematics, Statistics and Computer Science,Semnan University,Semnan,Iran;3.Women’s University of Semnan (Farzanegan),Semnan,Iran |
| 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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