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  • 1 School of Mathematics, Yangzhou University, Yangzhou 225002, P.R. China
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Abstract

Let R be an associative ring with identity. An element xR is said to be weakly exchange if there exists an idempotent eR such that exR and 1−e∊(1−x)R or 1−e∊(1+x)R. The ring R is said to be weakly exchange if all of its elements are weakly exchange. In this paper an element-wise characterization is given, and it is shown that weakly-Abel weakly exchange rings are weakly clean. Moreover, a relation between unit regular rings and weakly clean rings is also obtained.

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