Weakly-Abel rings and weakly exchange rings
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- 作者：Junchao Wei (1)
- 关键词：weakly exchange ring ; unit regular ring ; clean ring ; 16A30 ; 16A50 ; 16E50 ; 16D30
- 刊名：Acta Mathematica Hungarica
- 出版年：2012
- 出版时间：December 2012
- 年：2012
- 卷：137
- 期：4
- 页码：254-262
- 全文大小：372KB
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1. School of Mathematics, Yangzhou University, Yangzhou, 225002, P.R. China - ISSN：1588-2632
文摘
Let R be an associative ring with identity. An element x?em class="a-plus-plus">R is said to be weakly exchange if there exists an idempotent e?em class="a-plus-plus">R such that e?em class="a-plus-plus">xR and 1?em class="a-plus-plus">e?1?em class="a-plus-plus">x)R or 1?em class="a-plus-plus">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.