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| 强左极小Abel环 | |
| 引用本文： | 成青松,汪兰英,魏俊潮.强左极小Abel环[J].扬州大学学报(自然科学版),2010,13(1). |
| 作者姓名： | 成青松 汪兰英 魏俊潮 |
| 作者单位： | 1. 扬州大学,数学科学学院,江苏扬州225002;淮海工学院数理科学系,江苏连云港222005 2. 扬州大学,数学科学学院,江苏扬州225002;南京邮电大学,吴江职业技术学院,江苏吴江215200 3. 扬州大学,数学科学学院,江苏扬州225002 |
| 基金项目： | 国家自然科学基金资助项目，江苏省普通高校研究生科研创新项目 |
| 摘 要： | 证明了如下结果:①环R是强左DS环当且仅当R是左DS环和强左极小Abel环;②设R为强左DS环,e2=e∈R为弱角幂等元,则eRe也是强左DS环;③R是强左极小Abel环当且仅当对每个e∈MEl(R),任意的a,b∈R,eab=eaeb;④强左极小Abel环的次直积也是强左极小Abel环;⑤R是强左DS环当且仅当对R的每个左极小元k,存在e∈MEl(R),使得Rk=l(1-e),l(k)=R(1-e);⑥R是左极小Abel环当且仅当对R的每个左极小元k,当k2=0时,对每个a∈R,总有Rk+R(ka-1)=R. |
| 关 键 词： | 左极小元 强左极小Abel环 强左DS环 弱角幂等元 |
Strongly left min-abel rings |
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| CHENG Qing-song,WANG Lan-ying,WEI Jun-chao.Strongly left min-abel rings[J].Journal of Yangzhou University(Natural Science Edition),2010,13(1). | |
| Authors: | CHENG Qing-song WANG Lan-ying WEI Jun-chao |
| Institution: | CHENG Qing-song1,3,WANG Lan-ying1,2,WEI Jun-chao1*(1.Sch of Math Sci,Yangzhou Univ,Yangzhou 225002,China,2.NUPT Wujiang Voc Tech Coll,Wujiang 215200,3.Dept of Math & Phys,Huaihai Inst of Tech,Lianyungang 222005,China) |
| Abstract: | It is shown that ① A ring R is strongly left DS if and only if R is a left DS strongly left min-abel ring; ② Let R be a strongly left DS ring and e~2 =e∈R. If e is a weakly corner idempotent of R, then eRe is a strongly left DS ring; ③R is a strongly left min-abel ring if and only if for any e ∈ME_l(R) and a,b∈R, eab = eaeb;④ The subdirect product of strongly left min-abel rings is again a strongly left min-abel; ⑤ R is a strongly left DS ring if and only if for every left minimal element k of R, there exists e ∈NE_l(R) such that Rk = l(1-e) ,l(k) =R(1-e); ⑥ R is a left min-abel ring if and only if for every left minimal element k of R, if k~2 =0,then for each a∈R, Rk+R(ka-1)=R. |
| Keywords: | left minimal elements strongly left min-abel rings strongly left DS rings weakly corner idempotents |
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