Separative Ideals,Clean Elements,and Unit-Regularity |
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| Authors: | Huanyin Chen |
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| Institution: | 1. Department of Mathematics , Zhejiang Normal University , Jinhua, China chyzxl@hunnu.edu.cn |
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| Abstract: | ABSTRACT We prove that an ideal I of a regular ring R is separative if and only if each a ? R satisfying Rr(a)aR = Ra?(a)R = RaR(1 ? a)R ? I is unit-regular. If I is a separative ideal of a regular ring R, then each a ? R satisfying Rar(a2) = ?(a2)aR = R(a ? a2) R ? I is clean. Some applications are also obtained. |
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| Keywords: | Clean elements Regular ring Separative ideal |
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