The Maximal Graded Left Quotient Algebra of a Graded Algebra1)

We construct the maximal graded left quotient algebra of every graded algebra A without homogeneous total right zero divisors as the direct limit of graded homomorphisms （of left A-modules） from graded dense left ideals of A into a graded left quotient algebra of A. In the case of a superalgebra, and with some extra hypothesis, we prove that the component in the neutral element of the group of the maximal graded left quotient algebra coincides with the maximal left quotient algebra of the component in the neutral element of the group of the superalgebra.     

Tilting objects on tubular weighted projective lines: A cluster tilting approach

Using the cluster tilting theory,we investigate the tilting objects in the stable category of vector bundles on a weighted projective line of weight type(2,2,2,2).More precisely,a tilting object consisting of rank-two bundles is constructed via the cluster tilting mutation.Moreover,the cluster tilting approach also provides a new method to classify the endomorphism algebras of the tilting objects in the category of coherent sheaves and the associated bounded derived category.     

倾斜对中的倾斜双模

Tilting pair was introduced by Miyashita in 2001 as a generalization of tilting module. In this paper, we construct a tilting left Endh（C）-right Endh（T）-bimodule for a given tilting pairs （C,T） in modh, where A is an Artin algebra.     

REPETITIVE CLUSTER-TILTED ALGEBRAS

Let H be a finite-dimensional hereditary algebra over an algebraically closed field k and C F m be the repetitive cluster category of H with m ≥ 1. We investigate the properties of cluster tilting objects in C F m and the structure of repetitive clustertilted algebras. Moreover, we generalize Theorem 4.2 in [12] (Buan A, Marsh R, Reiten I. Cluster-tilted algebra, Trans. Amer. Math. Soc., 359(1)(2007), 323-332.) to the situation of C F m , and prove that the tilting graph KCFm of C F m is connected.     

主拟-Baer模

In this paper, we give the equivalent characterizations of principally quasi-Baer modules, and show that any direct summand of a principally quasi-Baer module inherits the property and any finite direct sum of mutually subisomorphic principally quasi-Baer modules is also principally quasi-Baer. Moreover, we prove that left principally quasi-Baer rings have Morita invariant property. Connections between Richart modules and principally quasi-Baer modules are investigated.     

The socle of the last term in a minimal injective resolution

Let Λ and Γ be left and right Noetherian rings and Λ U a generalized tilting module with Γ = End( Λ U ). For a non-negative integer k, if Λ U is (k - 2)-Gorenstein with the injective dimensions of Λ U and U Γ being k, then the socle of the last term in a minimal injective resolution of Λ U is non-zero.     

Generalized Green Correspondence of Graded Modules

The author studies the Green correspondence and quasi-Green correspondence for indecomposable modules over strongly graded rings. The motivation is to investigate the influence of induction and restriction processes on indecomposability of graded modules.     

关于余倾斜双模的k-挠自由模

Let A and F be left and right Noetherian rings and ∧ωr a cotilting bimodule. A necessary and sufficient condition for a finitely generated A-module to be ω-k-torsionfree is given and the extension closure of Tω^i is discussed. As applications, we give some results of ∧ωr related to l.id（ω） ≤ k.     

Modules and Structure Presheaves for Arbitary Rings

Basic techniques in the classical theory of commutative associative rings A with unity are:(i) The homological characterization of A in the category of A-modules. (ii) The rings of quotients of prime or semjprime rings A,(iii) The localization Ap at a prime ideal P and the structure sheaf on the prime spectrum of A. All these parts of structure theory are closely related to each other in this case.While technique (i) was successfully applied to non-commutative rings, the parts (ii) and (iii) do not allow a satisfying extension to this more general situation. Moreover, in the special cases which admit corresponding constructions, the interplay between the different points usually gets lost.Replacing the cateaory of left A-modules by a suitable subcategory σ[A] of bimodules over an arbitary (non-associative) ring A a natural extension of all three techniques under consideration which preserves relationships known from the classical situation is obtainedPart (i) and (ii) of the resulting theory can be fou     

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.     

A Construction of Characteristic Tilting Modules

Associated with each finite directed quiver Q is a quasi-hereditary algebra, the so-called twisted double of the path algebra kQ. Characteristic tilting modules over this class of quasi-hereditary algebras are constructed. Their endomorphism algebras are explicitly described. It turns out that this class of quasi-hereditary algebras is closed under taking the Ringel dual. Received November 15, 2000, Accepted March 5, 2001     

Hom-Orthogonal Partial Tilting Modules for Dynkin Quivers

We count the number of isomorphism classes of hom-orthogonal partial tilting modules over path algebras of Dynkin quiver of type 𝔸 _n , 𝔻 _n , 𝔼 _n . This number is independent on the choice of an orientation of the arrows, and the number for 𝔸 _n or 𝔻 _n -type can be expressed as a special value of a hypergeometric function. As a consequence of our theorem, we obtain a minimum value of the number of basic relative invariants of corresponding regular prehomogeneous vector spaces.     

Dn型路代数本性倾斜模的一个必要条件

倾斜理论是研究代数表示理论的重要工具之一．本文主要对Dn（n≥4），E6，E7，E8型路代数倾斜模在其对应的AR-箭图上的结构持点进行研究．通过对Dn（n≥4），上E6，E7，E8型路代数A的AR-箭图ΓA分析证明了Dn≥4），E6，E7，E8型路代数本性慨斜模TA的一个必要条件是：在A的AR-箭图ΓA的每个边缘的r-轨道都有TA的不可分解直和项对应的点．     

Canonical Tilting Modules Over Shod Algebras are Regular in Codimension One

We show that for a class of modules over shod algebras, including the canonical tilting modules, the closures of the corresponding orbits in module varieties are regular in codimension one.     

具有性质(G'_k)的Wakamatsu倾斜模

本文引进了具有性质(G'k)的Wakamatsu倾斜模的概念,并用同调有限子范畴的性质对其进行了刻画．     

Tilting Modules Over Quasi-Hereditary Nakayama Algebras #

The structure of Ringel duals of quasi-hereditary Nakayama algebras and of quasi-hereditary left serial algebras is described.     

An型路代数倾斜模的个数

本文证明APR-倾斜过程不改变Dynkin型路代数的倾斜模的个数,并给出计算An型 路代数的倾斜模的个数的递推公式.     

具有性质(G'_k)的Wakamatsu倾斜模

本文引进了具有性质(G'k)的Wakamatsu倾斜模的概念,并用同调有限子范畴的性质对其进行了刻画．     

具有性质$(G_k)$的Wakamatsu倾斜模

本文引进了具有性质(Gk)的Wakamatsu倾斜模的概念,并用同调有限子范畴的性质对其进行了刻画．所得结果推广了黄兆泳在文献[1]和[11]中的工作．