| J-clean环的推广 |
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| 引用本文： | 崔建,秦龙.J-clean环的推广[J].数学进展,2020(1):29-38. |
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| 作者姓名： | 崔建 秦龙 |
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| 作者单位： | 安徽师范大学数学系 |
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| 基金项目： | This research is supported by NSFC(No.11401009);A nhui Provincial Natural Science Foundation(No.1408085QA01). |
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| 摘 要： | 如果R中每个元素(对应地,可逆元)均可表示为一个幂等元与环R的Jacobson根中一个元素之和,则称环R是J-clean环(对应地,UJ环).所有的J-clean环都是UJ环.作为UJ环的真推广,本文引入GUJ环的概念,研究GUJ环的基本性质和应用.进一步地,研究每个元素均可表示为一个幂等元与一个方幂属于环的Jacobson根的元素之和的环.
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| 关 键 词： | CLEAN环 J-clean环 UJ环 诣零clean环 GJ-clean环 |
Generalizations of J-clean Rings |
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| CUI Jian,QIN Long.Generalizations of J-clean Rings[J].Advances in Mathematics,2020(1):29-38. |
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| Authors: | CUI Jian QIN Long |
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| Institution: | (Department of Mathematics,Anhui Normal University,Wuhu,Anhui,241002,P.R.China) |
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| Abstract: | A ring R is J-clean(respectively,UJ) if every element(respectively,unit) of R is a sum of an idempotent and an element from the Jacobson radical of R.All J-clean rings are UJ rings.In this paper,we introduce the notion of a GUJ ring,which is a proper generalization of UJ rings.The properties and applications of GUJ rings are discussed.We also investigate rings for which every element is a sum of an idempotent and an element whose power belongs to the Jacobson radical. |
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| Keywords: | clean ring J-clean ring UJ ring nil clean ring GJ-clean ring |
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