共查询到20条相似文献,搜索用时 78 毫秒
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An associative ring R with identity is semiperfect if and only if every element of R is a sum of a unit and an idempotent, and R contains no infinite set of orthogonal idempotents. A ring which contains no infinite set of orthogonal idempotents is an exchange ring if and only if every element is a sum of a unit and an idempo-tent 相似文献
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The Jacobson Property of Group Rings and Its GeneralizationsZhuYuansen(朱元森)andwangZhixi(王志玺)(DepartmentofMathematics,HebeiTea... 相似文献
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On Decompositions of Quasi-Regular Rings 总被引:1,自引:0,他引:1
Hu Xianhui 《东北数学》1994,(2)
OnDecompositionsofQuasi-RegularRings¥HuXianhui(胡先惠)(DepartmntofMathematics,theCentralInstituteofNationalities,Beijing,100081)... 相似文献
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Zhang Jule 《东北数学》1998,(1)
in this paper, new characteristic properties of strongly regular rings are' given.Relations between certain generalizations of duo rings are also considered. The followingconditions are shown to be equivalent: (1) R is a strongly regular ring; (2) R is a left SFring such that every product of two independent closed left ideals of R is zero; (3) R is aright SF-ring such that every product of two independent closed left ideals of R is zero; (4)R is a left SF-ring whose every special left annihilator is a quasi-ideal; (5) R is a right SFring whose every special left annihilator is a quasi-ideal; (6) R is a left SF-ring whose everymaximal left ideal is a quasi-ideal; (7) R is a right SF-ring whose every maximal left ideal isa quasi-ideal; (8) R is a left SF-ring such that the set N(R) of all nilpotent elements of R isa quasi-ideal; (9) R is a right SF-ring such that N(R) is a quasi-ideal. 相似文献
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Excellent Extensions of RingsLiuZhongkui(刘仲奎)andWangTingZhen(王廷桢)(DepartmentofMathcmatics,NorthwestNormalUniversity,Lanzhon,7... 相似文献
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Hua-Ping Yu 《代数通讯》2013,41(6):2187-2197
An associative ring R with identity is said to have stable range one if for any a,b? R with aR + bR = R, there exists y ? R such that a + by is left (equivalently, right) invertible. The main results of this note are Theorem 2: A left or right continuous ring R has stable range one if and only if R is directly finite (i.e xy = 1 implies yx = 1 for all x,y ? R), Theorem 6: A left or right N 0o-quasi-continuous exchange ring has stable range one if and only if it is directly finite, and Theorem 12: left or right N 0-quasi-continuous strongly π-regular rings have stable range one. Theorem 6 generalizes a well-known result of Goodearl [10], which says that a directly finite, right N o-continuous von Neumann regular ring is unit-regular 相似文献
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Chen Huanyin 《东北数学》1999,(2)
LetRbeanassociativeringwithidentity.ArightR-moduleAissaidtosatisfyfiniteexchangepropertyifforeveryrightR-moduleKandanytwodeco... 相似文献
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Wang Fuzheng 《东北数学》1995,(2)
Approximately Cohen-Macaulay Rings and Samuel FunctionsWangFuzheng(王福正)(DepartmentofMathematics,PeikingUniversityBeijing,1008... 相似文献
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对粗糙集上代数结构进行了研究,引入了粗糙除环、粗糙域和粗糙整环等概念.利用粗糙集理论方法和经典代数中的处理手段,讨论了粗糙除环和它们的结构特征,得到了它们的一些良好的性质. 相似文献
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Chen Huanyin 《东北数学》1997,(1)
RingsoverwhichInvertibleModulesareFreeChenHuanyin(陈焕艮)(DepartmentofMathematics,HunanNormalUniversity,Changsha,410006)Abstract... 相似文献
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半素环的几个交换性条件 总被引:7,自引:0,他引:7
一个半素环 R是交换环当且仅当 R满足下列条件之一 :( ) (xmy) n+xmy∈ Z(R) ,对任意的 x ,y∈ R。( ) (xmy) n- yxm∈ Z(R) ,对任意的 x,y∈ R。( ) (xmy) n+yxm∈ Z(R) ,对任意的 x,y∈ R。其中 m,n是固定的正整数且 n >1 相似文献
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P. R. Fuchs C. J. Maxson G. F. Pilz 《Transactions of the American Mathematical Society》1997,349(3):1271-1284
In this paper we investigate the problem of characterizing those rings such that every nonzero polynomial with coefficients from has a finite number of zeros in . Particular attention is directed to the class of skew polynomial domains.
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