关于Unit J-clean环（英文）  

On Unit J-clean Rings

作　　者：沈洪地 陈焕艮[1] 

机构地区：[1]杭州师范大学理学院,浙江杭州310036

出　　处：《杭州师范大学学报（自然科学版）》2016年第2期163-170,共8页Journal of Hangzhou Normal University(Natural Science Edition)

基　　金：the Natural Science Foundation of Zhejiang Province(LY13A010019)

摘　　要：一个元素叫做右单位J-clean(左单位J-clean)如果在R中存在一个单位u,使得au(ua)是J-clean的.一个环R叫做右单位J-clean(左单位J-clean)环当且仅当环中的每个元素都是右单位J-clean(左单位J-clean)的.文章得到了以下几个结论:每个J-clean环是unit J-clean环,每个unit J-clean环是unit clean环,每个2-good环是unit clean环,但是以上三个结论反过来就不正确.文章还证明了一个unit J-clean环,那么它是2-good环当且仅当1能表示成两个单位的和.当R是一个阿贝尔环,I是一个R的包含在Jacobson根里的理想,那么R是unit J-clean环当且仅当(1)R/I是unit J-clean的.(2)幂等元关于J(R)可提升.An element a∈Rright（left）unit J-clean if there is a unit u∈Rsuch that au（ua）is J-clean.A ring Ris called right（left）unit J-clean if each element is right（left）unit J-clean.In this paper,we get the results that every J-clean ring is unit J-clean,every unit J-clean is unit clean and every 2-good ring is unit clean but the converse of all the three conclusions are not true.Further,we prove that for a unit J-clean ring Ris 2-good if and only if 1=u＋vfor some u,v∈U（R）.Also when Ris an abelian ring,Iis an ideal of Rand IJ（R）,then Ris unit J-clean if and only if（1）R/Iis unit J-clean.（2）Idempotents lift modulo J（R）.

关 键 词：J-clean环 UNIT J-clean环 幂等元 JACOBSON根 

分 类 号：O153.3[理学—数学]