共查询到17条相似文献,搜索用时 265 毫秒
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设R和S是环,U是平坦右R-模,V是平坦右S-模.本中我们证明了(N,(U,V))-lc.dim(R S)=sup((N,U)-lc.dimR,(N,V)-lc.dimS). 相似文献
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刻划了弱闭T(N)-模中Schatten类之间的等距线性满映射.设U、W分别为由左连续序同态N→和N→所确定的弱闭T(N)-模.Φ为U∩Cp到W∩Cp(1≤p<∞,p≠2)上的等距线性映射.若(0)+=(0),H-=H且min{dim(0),dim(0)#,dim(HH~),dim(HH∧)}≥2,则存在到的等距Ui(i=1,2)及酉算子Vi(i=1,2),使得Φ(A)=U1AV1或Φ(A)=V2AU2. 相似文献
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ZhongKuiLIU JavedAHSAN 《数学学报(英文版)》2004,20(1):105-114
Let U be a flat right R-module and N an infinite cardinal number.A left R-module M is said to be (N,U)-coherent if every finitely generated submodule of every finitely generated M-projective module in σ[M] is (N,U)-finitely presented in σ[M].It is proved under some additional conditions that a left R-module M is (N,U)-coherent if and only if Л^Ni∈I U is M-flat as a right R-module if and only if the (N,U)-coherent dimension of M is equal to zero.We also give some characterizations of left (N,U)-coherent dimension of rings and show that the left N-coherent dimension of a ring R is the supremum of (N,U)-coherent dimensions of R for all flat right R-modules U. 相似文献
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Let S be an excellent extension of a ring R and U a flat right S-module. We show in this paper that the left (N,U)-coherent dimension of S is equal to that of R. 相似文献
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弱闭T(N)-模的预零化子的等距映射 总被引:1,自引:0,他引:1
本文刻划了弱闭T(N)-模的预零化子间的等距映射.设u,W分别为由左连续序同态N→~N和N→~N所确定的弱闭T(N)-模, u(?),W(?)分别为u,W的预零化子,Φ为由u(?)到W(?)上的线性等距映射.若(0)*=(0)#=(0),dim(0)+≠1且min{dim(H(?)~H),dim(He(?)^H)}≥2,则存在酉算子Ui,Vi(i=1,2),使得Φ(A)=U1AV*1或Φ(A)=U2A*V2*. 相似文献
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本文刻画了弱闭T(N)-模的预零化子的线性等距映象群的无穷小生成元.设U为由N到N的左连续序同态N到N所确定的弱闭T(N)-模,U_⊥为U的预零化子。{Φ_t :t∈R}为U_⊥到U_⊥上的单参数强连续线性等距映象群。若(0)_*=(0),dim(0)+≠1且H_-=H,dim(HH)≥ 2,则存在有界自伴算子K_1,K_2使得{Φ_t :t∈R}的无穷小生成元为α(X)=i(K_1X-XK_2)。 相似文献
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引进了一新模类-完全平坦模(每一个商模平坦).并得到了:令M是平坦左R-模,RM是完全平坦模当且仅当RM的所有子模是纯的当且仅当每一个右R-模A是M-平坦的.同时本文用完全平坦模刻画了V.N.正则环. 相似文献
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S-内射模及S-内射包络 总被引:1,自引:0,他引:1
设R是环.设S是一个左R-模簇,E是左R-模.若对任何N∈S,有Ext_R~1(N,E)=0,则E称为S-内射模.本文证明了若S是Baer模簇,则关于S-内射模的Baer准则成立;若S是完备模簇,则每个模有S-内射包络;若对任何单模N,Ext_R~1(N,E)=0,则E称为极大性内射模;若R是交换环,且对任何挠模N,Ext_R~1(N,E)=0,则E称为正则性内射模.作为应用,证明了每个模有极大性内射包络.也证明了交换环R是SM环当且仅当T/R的正则性内射包e(T/R)是∑-正则性内射模,其中T=T(R)表示R的完全分式环,当且仅当每一GV-无挠的正则性内射模是∑-正则性内射模. 相似文献
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Let S be an excellent extension of a ring R and U a flat right 5-module. We show in this paper that the left (N, U)-coherent dimension of S is equal to that of R. 相似文献
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Let R be a ring. A fight R-module M is called f-projective if Ext^1 (M, N) = 0 for any f-injective right R-module N. We prove that (F-proj,F-inj) is a complete cotorsion theory, where (F-proj (F-inj) denotes the class of all f-projective (f-injective) right R-modules. Semihereditary rings, von Neumann regular rings and coherent rings are characterized in terms of f-projective modules and f-injective modules. 相似文献
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文章对$3\times 3$阶三角矩阵环$$\Gamma = \left(\begin{array}{ccc}T & 0 & 0 \\M & U & 0\\{N \otimes _U M} & N & V \\\end{array}\right)$$上的模作了研究,其中T,U,V均是环, M,N分别是U-T, V-U双模.通过用一个五元组$(A,B,C;f,g)$来描述一个左$\Gamma$-模 (其中$A \in \mod T, B\in {\rm mod} U, C \in {\rm mod} V$, $f:M \otimes _T A \to B \in {\rm mod} U, g:N \otimes _U B \to C \in {\rm mod} V$), 文章分别刻画了$\Gamma$上的一致模、空的模、有限嵌入模,并且确定了${ }_\Gamma (A \oplus B \oplus C)$的根和基座. 相似文献
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设R■A是环的Frobenius扩张,其中A是右凝聚环,M是任意左A-模.首先证明了_AM是Gorenstein平坦模当且仅当M作为左R-模也是Gorenstein平坦模.其次,证明了Nakayama和Tsuzuku关于平坦维数沿着Frobenius扩张的传递性定理的"Gorenstein版本":若_AM具有有限Gorenstein平坦维数,则Gfd_A(M)=Gfd_R(M).此外,证明了若R■S是可分Frobenius扩张,则任意A-模(不一定具有有限Gorenstein平坦维数),其Gorenstein平坦维数沿着该环扩张是不变的. 相似文献
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Dong Zhe 《Proceedings of the American Mathematical Society》2007,135(1):191-200
In this paper, we first introduce the concept of single elements in a module. A systematic study of single elements in the Alg-module is initiated, where is a completely distributive subspace lattice on a Hilbert space . Furthermore, as an application of single elements, we study module isomorphisms between norm closed Alg-modules, where is a nest, and obtain the following result: Suppose that are norm closed Alg-modules and that is a module isomorphism. Then and there exists a non-zero complex number such that .
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研究了$(m,d)$-内射$R$-模作成的类是(预)盖类的条件,证明了$(m,d)$-凝聚环上的每一个左$R$-模都具有$(m,d)$-内射盖.在此基础上,又引入研究了Gorenstein $(m,d)$-平坦模和Gorenstein $(m,d)$-内射模,证明了$(m,d)$-凝聚环上的左$R$-模$M$是Gorenstein$(m,d)$-平坦模的充分必要条件是它的特征模$M^{+}$是Gorenstein $(m,d)$-内射模.推广了Goresntein平坦模和Goresntein $n$-平坦模上的一些结果. 相似文献
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In this paper, let m, n be two fixed positive integers and M be a right R-module, we define (m, n)-M-flat modules and (m, n)-coherent modules. A right R-module F is called (m, n)-M-flat if every homomorphism from an (n, m)-presented right R-module into F factors through a module in addM. A left S-module M is called an (m, n)-coherent module if MR is finitely presented, and for any (n, m)-presented right R-module K, Hom(K, M) is a finitely generated left S-module, where S = End(MR). We mainly characterize (m, n)-coherent modules in terms of preenvelopes (which are monomorphism or epimorphism) of modules. Some properties of (m, n)-coherent rings and coherent rings are obtained as corollaries. 相似文献