共查询到18条相似文献,搜索用时 203 毫秒
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对于完备格L上给定的|I|×|I|的矩阵R,若存在|I|×|I|的L上的矩阵S满足S☉S=R,则称S为R的平方根,其中|I|表示指标集I的基数,☉在本文中指的是sup-(J)合成算子并且(J)是无限Ⅴ分配的保序的算子,本文给出了完备格上基于sup-(J)合成算子的矩阵平方根存在的充要条件以及相应的理论上的算法求解所有的平方根. 相似文献
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有限正规扩张的几种根 总被引:2,自引:0,他引:2
欧海文 《数学年刊A辑(中文版)》1992,(3)
本文讨论根性p=B,s,J,U依次表示Baer-根、强质根、Jacobson-根,Browa-McCoy-根),并得到了关于等式p(S)=S·p(R)对环R成立的几类有限正规扩张S。 相似文献
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主要证明了:(i)假设R是右广义半正则右ACS-环,若J(R)∩I=J(I)对于R的任意右理想I都成立,则J(R)=Z(RR);(ii)如果R是右AP-内射环且R的每个奇异单右R-模是GP-内射,则对于R的任意右理想I都有J(R)∩I=J(I). 相似文献
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引言 设K={O,1_k,a,b,c,…}为有单位元1_k的可换环,R={O,|σ∈∑}、S={O,1_s,S_r|τ∈Γ}分别为有单位元1_R、1_s的K环,当然1_k1_R=1_R=1_R1_k,1_k1_s=1_s=1_s1_k,下面在不至于混淆的情况下,1_k、1_R、1_s均用1表示。M={x_λ|λ∈∧}、M'={u_i|i∈I}为左R酉模,N={y_u|μ∈Ω}、N'={U_i|i∈J}为左S酉模。我们用H_R(M,M')表示R模M到R模M'的所有R同态所形成的可换群。文[1]将R模M与S模N的张量积定义为一个左R S模,本文就在此基础上讨论M N作为R S模的一些性质及其线性映射。如果不特别声明,本文中所有的环都有单位元,所有的模都指左酉模。 相似文献
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设S为有限局部单位元半群,R为S—分次环.首先定义了S—分次环R在半群S上的冲积R#S*,证明了模范畴R#S*-M od与分次模范畴(S,R)-g r之间的等价性,并进一步研究了局部单位元半群分次环的分次Jacobson根及其相关的自反根的关系,得到重要关系式J(R#S*)=JS(R)#S*及Jref(R)=(J(R#S*))↓=JS(R). 相似文献
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The structure of a class of Z-local rings 总被引:1,自引:0,他引:1
WU Tongsuo & LU Dancheng Department of Mathematics Shanghai Jiao Tong University Shanghai China Department of Mathematics Suzhou University Suzhou China 《中国科学A辑(英文版)》2006,49(10)
A local ring R is called Z-local if J(R) = Z(R) and J(R)2 = 0. In this paper the structure of a class of Z-local rings is determined. 相似文献
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我们考虑非线性规划问题(P)■f(x),其中R={x|Ax=a,Bx≤b},A是p×n矩阵,其秩为p,B是q×n矩阵,x∈E~n,a∈E~p,b∈E~q,f(x)∈C~1.我们以R~*表示(P)的最优解集合,并假定R非空.最近,M.S.Bazaraa与J.J.Goode 相似文献
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Let R and S be two vectors with m and n nonnegative integers as conponents respectively. Let u(R, S) be the class consisting of all m×n (0,1) - matrices with row sum vector R and column sum vector S. Suppose that A is the maximal mrixat with row sum vector R. Let S he the column sum vector of A. (of. H. J. Ryser, Combinatorial Mathematics, Carcus Math. Monograph 14 (1963)). Let L(S)={S=(s1,…,sm),S-1≥s2≥…≥sn}, and let F(R, S) be the cardinal function of u(R,S), i. e.. f(R, S) = |u(R, S) |. Then L(S) is the nonzero-point set of f(R,S). In this paper our principal result is the following. 相似文献
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Let R be a commutative Noetherian ring, I and J be two ideals of R, and M be an R-module. We study the cofiniteness and finiteness of the local cohomology module HiI,J(M) and give some conditions for the finiteness of HomR(R/I, HsI,J(M)) and Ext1R(R/I, HsI,J(M)). Also, we get some results on the attached primes of HdimMI,J (M). 相似文献
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Let R be an associative ring with identity.R is said to be semilocal if R/J(R)is(semisimple)Artinian,where J(R)denotes the Jacobson radical of R.In this paper,we give necessary and sufficient conditions for the group ring RG to be semilocal,where G is a locally finite nilpotent group. 相似文献
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We study the vibration of an elastic thin shell which is pre-constrained by a large displacement with a small deformation. In this first Note we prove the solutions exist and we investigate both the interior regularity and the boundary regularity which is known to be important in the shape differentiation of hyperbolic equations. To cite this article: J. Cagnol, J.-P. Zolésio, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 161–166 相似文献
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J-semicommutative环的性质 总被引:1,自引:0,他引:1
环冗称为J—semicommutative若对任意B,b∈R由ab=0可以推得aRb∈J(R),这里J(R)是环R的Jacobson根.环R是J—semicommutative环当且仅当它的平凡扩张是J—semicommutative环当且仅当它的Don'oh扩张是J—semicommutative环当且仅当它的Nagata扩张是,一semicommutative环当且仅当它的幂级数环是J—semicommutative环.若R/J(R)是semicommutative环,则可得到R是J-semicommutative环.本文进一步论证了如果,是环月的一个幂零理想,且R/I是J—semicommutative环,则R也是J-semicommutative环最后给出了J—semicommutative环与其他一些常见环的联系 相似文献
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《代数通讯》2013,41(8):2489-2497
Let (R. m) be a d-dimensional Cohen-Macaulay local ring. Given m-primary ideals J ? I of R such that I is contained in the integral closure of J and λ(I/J)= I, we compare depth G(J) and depth G(J). For example, if J has reduction number one, JI = I2, and μ(J)≤ d + 1, we prove that depth G(I)≥d – 1. If, in addition, μ(I)= d + 1, we show that I has reduction number one, and hence G(I) is Cohen-Macaulay. These results, besides leading to statements comparing depths of associated graded rings along a composition series, make visible the possibility of studying powers of an ideal by using reductions that are not minimal reductions. 相似文献
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For ordinals α beginning a Σ1 gap in $\mathrm{L}(\mathbb {R})$, where $\Sigma _{1}^{\mathrm{J}_{\alpha }(\mathbb {R})}$ is closed under number quantification, we give an inner model‐theoretic proof that every thin $\Sigma _{1}^{\mathrm{J}_{\alpha }(\mathbb {R})}$ equivalence relation is $\Delta _{1}^{\mathrm{J}_{\alpha }(\mathbb {R})}$ in a real parameter from the (optimal) hypothesis $\mathsf {AD}^{\mathrm{J}_{\alpha }(\mathbb {R})}$. 相似文献