Some Properties of Artin-Rees Modules and Rings

The class of Artin-Rees modules is large.It contains modules satisfying (accr).In this paper, we investigate such modules and show that some properties of modules satisfying (accr) can be generalized to modules of this class.     

关于对偶模的平坦性和内射性(Ⅱ)

对交换环Ｒ和Ｂ－模范畴上的一个内射余生成元Ｂ,我们用相对于Ｅ的对偶模的性质刻画了ＱＦ环,ＩＦ环和半遗传环．     

Some Rings Characterized by Modules

ＳｏｍｅＲｉｎｇｓＣｈａｒａｃｔｅｒｉｚｅｄｂｙＭｏｄｕｌｅｓ￥ＹａｏＺｈｏｎｇｐｉｎｇ；ＷａｎｇＤｉｎｇｇｕｏ（ＬｉａｏｃｈｅｎｇＴｅａｃｈｅｒ＇ｓＣｏｌｌｅｇｅ，Ｌｉａｏｃｈｅｎｇ２５２０５９）（ＱｕｆｕＮｏｒｍａｌＵｎｉｖｅｒａｌｔｙ，Ｑｕｆｕ...     

Relative weak injectivity of operator system pairs

The concept of a relatively weakly injective pair of operator systems is introduced and studied in this paper, motivated by relative weak injectivity in the C*-algebra category. E. Kirchberg [11] proved that the C^?${\mathrm{C}}^{?}$-algebra C^?(_F∞)${\mathrm{C}}^{?}({\mathbb{F}}_{\infty })$ of the free group _F∞${\mathbb{F}}_{\infty }$ on countably many generators characterises relative weak injectivity for pairs of C^?${\mathrm{C}}^{?}$-algebras by means of the maximal tensor product. One of the main results of this paper shows that C^?(_F∞)${\mathrm{C}}^{?}({\mathbb{F}}_{\infty })$ also characterises relative weak injectivity in the operator system category. A key tool is the theory of operator system tensor products  and .     

相关Hopf模的对偶

本文的目的就是给出相关Hopf模的对偶性质.在第一部分,证明了相关Hopf模的对偶模仍是相关Hopf模.特别地,Hopf模的对偶仍是Hopf模.在第二、第三两部分,分别给出相关Hopf模的对偶相关Hopf模的基本结构定理及Maschke定理.     

Relative Regular Modules. Applications to von Neumann Regular Rings

We use the concept of a regular object with respect to another object in an arbitrary category, in order to obtain the transfer of regularity in the sense of Zelmanowitz between the categories R −mod and S −mod, when S is an excellent extension of the ring R. Consequently, if S is an excellent extension of the ring R, then S is von Neumann regular ring if and only if R is also von Neumann regular ring. In the second part, using relative regular modules, we give a new proof of a classical result: the von Neumann regular property of a ring is Morita invariant.     

Relative Completions of Linear Groups Over Coordinate Rings of Curves

We compute the completion of the special linear group over the coordinate ring A of a curve over a number field k relative to its representation in SL _n (A/𝔪), for 𝔪 a maximal ideal.     

相关Yetter-Drinfel’d模和扭曲Hopf模及其基本结构定理

本文引入了扭曲余模概念,给出了由扭曲余模构造的扭曲Hopf模的判别条件及其基本结构定理,引入了相关Yetter-Drinfel’d模概念(它是Yetter-Drinfel’d模概念的自然推广),证明了相关Yetter-Drinfel’d模范畴是预辫monoidal范畴,指出了由Yetter-Drinfel’d模通过扭曲余模构作的模恰是相关Yetter-Drinfel’d模.     

On the Cohomology of Relative Hopf Modules

Let H be a Hopf algebra over a field k, and A an H-comodule algebra. The categories of comodules and relative Hopf modules are then Grothendieck categories with enough injectives. We study the derived functors of the associated Hom functors, and of the coinvariants functor, and discuss spectral sequences that connect them. We also discuss when the coinvariants functor preserves injectives.     

Orthogonality Matrices for Modules over Finite Frobenius Rings and MacWilliams' Equivalence Theorem

MacWilliams' equivalence theorem states that Hamming isometries between linear codes extend to monomial transformations of the ambient space. One of the most elegant proofs for this result is due to K. P. Bogart et al. (1978, Inform. and Control37, 19–22) where the invertibility of orthogonality matrices of finite vector spaces is the key step. The present paper revisits this technique in order to make it work in the context of linear codes over finite Frobenius rings.     

Relative Projective Modules and Relative Injective Modules

Let R be a ring, and n and d fixed non-negative integers. An R-module M is called (n, d)-injective if Ext ^d+1 _R (P, M) = 0 for any n-presented R-module P. M is said to be (n, d)-projective if Ext¹ _R (M, N) = 0 for any (n, d)-injective R-module N. We use these concepts to characterize n-coherent rings and (n, d)-rings. Some known results are extended.     

Associated and Attached Primes of Some Graded Modules Over Semigroup Rings

In this paper, algebras are finite dimensional over an algebraically closed field k, and modules are k-finite dimensional left modules. We prove the stable equivalence conjecture for algebras stably equivalent to algebras A with the following conditions: basic, connected and selfinjective; rad³A = 0 but rad²A ¬ 0; and the separated quiver Q³ _A of the quiver Q_A of A consisting of more than two connected components.     

Rings Related to Mininjective and Min-Flat Modules

R is called a left PS (resp. left min-coherent, left universally mininjective) ring if every simple left ideal is projective (resp. finitely presented, a direct summand of R). We first investigate when the endomorphism ring of a module is a PS ring, a min-coherent ring, or a universally mininjective ring. Then we characterize PS rings and universally mininjective rings in terms of endomorphisms of mininjective and min-flat modules. Finally, we study commutative min-coherent rings and (universally) mininjective rings using properties of homomorphism modules of special modules.     

Almost-Perfect Rings and Modules

Following [1 Amini , A. , Ershad , M. , Sharif , H. ( 2008 ). Rings over which flat covers of finitely generated modules are projective . Comm. Algebra 36 : 2862 – 2871 .[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]], a ring R is called right almost-perfect if every flat right R-module is projective relative to R. In this article, we continue the study of these rings and will find some new characterizations of them in terms of decompositions of flat modules. Also we show that a ring R is right almost-perfect if and only if every right ideal of R is a cotorsion module. Furthermore, we prove that over a right almost-perfect ring, every flat module with superfluous radical is projective. Moreover, we define almost-perfect modules and investigate some properties of them.     

On the Construction of d-Continuous Modules over Some Special Rings

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A Note on Rings and Modules Graded by Some Special Groups

In this note we prove that the prime madicals of some graded rings and the scoles of some graded modules are also graded. The results on the relations between the prime radical and the graded prime radical are also presented. Moreover, the relations between a graded ring and its initial subring are studied.     

关于中心对称矩阵的几个性质

利用中心对称矩阵定义及翻转矩阵Vn等技巧,给出中心对称矩阵的一些性质和O≠X∈Cn与VnX同为中心对称矩阵对应于同一特征值的特征向量等结论.     

Modules whose Endomorphism Rings have Finite Triangulating Dimension and Some Applications

By defining orthogonal decomposition for modules, we prove that an R-module M has only finitely many fully invariant direct summands if and only if End _R (M) has triangulating dimension ${n = {\rm Sup}\{k \in \mathbb{N} | M = \oplus^{k}_{i=1}M_{i}}$ is left orthogonal}. Denoting n = τdim(M _R ), the triangulating dimension of M _R , it is shown that τ dim(M _R ) is Morita invariant, and when R is an Artinian principal ideal ring, τ dim(M _R ) is the number of socle components of M _R . If R is commutative then R is perfect (resp. a finite direct product of domains) if and only if it is semi-Artinian (resp. semiprime extending) with finite triangulating dimension. A recent result of Birkenmeier et al. [4] is generalized into a module setting.