强J-quasi-clean环  

Strongly J-quasi-clean Rings

作　　者：唐高华 臧乃策 赵汝菊 TANG Gao-hua;ZANG Nai-ce;ZHAO Ru-ju(School of Sciences,Beibu Gulf University,Qinzhou 535011,China;School of Mathematics and Statistics,Nanning Normal University,Nanning 530100,China)

机构地区：[1]北部湾大学理学院,广西钦州535011 [2]南宁师范大学数学与统计学院,广西南宁530100

出　　处：《南宁师范大学学报（自然科学版）》2023年第1期1-6,共6页Journal of Nanning Normal University：Natural Science Edition

基　　金：国家自然科学基金(12261001);广西自然科学基金(2021GXNSFAA220043,2022GXNSFBA035585);广西高校中青年教师科研基础能力提升项目(2022KY0423)。

摘　　要：该文引入了强J-quasi-clean环,并证明了强J-clean环是强J-quasi-clean环,而强J-quasi-clean环是强拟clean环,反过来都是不成立的;还证明了环R是强J-quasi-clean的当且仅当R/J(R)是拟Boole环且其每个拟幂等元都能强提升;最后指出强J-quasi-clean环是左(右)quasi-duo环.This paper introduces the notion of strongly J-quasi-clean ring.It is shown that strongly J-clean rings are strongly J-quasi-clean rings,and strongly J-quasi-clean rings are strongly quasi-clean rings,but neither of the converses of the two is true.Moreover,it is proved that a ring R is strongly J-quasi-clean if and only if R/J(R)is quasi-Boolean and each quasi-idempotent of R/J(R)can be strongly lifted.Finally we point out that strongly J-quasi-clean rings are left(right)quasi-duo rings.

关 键 词：强J-quasi-clean环 拟幂等元 强J-clean环 强拟clean环 JACOBSON根 

分 类 号：O153.3[理学—数学]