对偶扩张代数的shod子范畴与反变有限子范畴

设A是一个有限维代数,R是A的对偶扩张代数。本文研究代数R的shod子范畴,A-模范畴D的倾斜对象与R-模范畴D的倾斜对象之间的关系以及R的反变有限的子范畴。     

Coherent Functors and Covariantly Finite Subcategories

Given a locally presentable additive category A, we study a class of covariantly finite subcategories which we call definable. A definable subcategory arises from a set of coherent functors F _i on A by taking all objects X in A such that F _i X=0 for all i. We give various characterizations of definable subcategories, demonstrating that all covariantly finite subcategories which arise in practice are of this form. This is based on a filtration of the category of all coherent functors on A.     

两个相关代数上的一对同构模范畴

本文研究了Artin代数A与其子代数模范畴中反变有限子范畴之间的关系.利用范畴同构,获得了代数A上投射维数有限的子模范畴P∞(A)在有限生成的左A模范畴A-mod上反变有限的一个条件,推广了关于子范畴P∞(A)反变有限性的结果.     

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．     

Lattice Properties of Torsion Theories

The main purpose of this brief note is to show that the sets of all hereditary torsion theories which are noetherian, strongly noetherian, or of finite type, respectively, form a sublattice of the lattice of all hereditary torsion theories for the category R-mod.     

Torsion Theories and Primaty Decomposition of Modules

In this paper, the author obtains the following result: If R is a left semi-artinian max ring, then the primary decomposition theorem holds for all R-modules if and only if Ext (S_1, S_2) =0 for any non-isomorphic simple modules S_1 and S_2. By mecns of the primary decomposition of modules, the author proves: All torsion theories of \mu are simple type if and only if R is a left semi-artinian max ring and Ext(S_1, S_2)=0 for any non-isomorphic simple modules S_1, S_2.     

Perverse Coherent t-Structures Through Torsion Theories

Bezrukavnikov, later together with Arinkin, recovered Deligne’s work defining perverse t-structures in the derived category of coherent sheaves on a projective scheme. We prove that these t-structures can be obtained through tilting with respect to torsion theories, as in the work of Happel, Reiten and Smalø. This approach allows us to define, in the quasi-coherent setting, similar perverse t-structures for certain noncommutative projective planes.     

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．     

Layer Lengths, Torsion Theories and the Finitistic Dimension

Let $\mathcal{C}$ be a length-category. Generalizing the Loewy length, we propose the layer length associated with a torsion theory, which is a new measure for objects of $\mathcal{C}$ . As an application, we use the layer lengths and the Igusa–Todorov function to get a theorem (see Theorem 6.4) having as corollaries the main results of Huard et al. (Bull Lond Math Soc 41:367–376, 2009) and Wang (Commun Algebra 22(7):419–449, 1994).     

Representation Dimension as a Relative Homological Invariant of Stable Equivalence

Over an Artin algebra Λ many standard concepts from homological algebra can be relativized with respect to a contravariantly finite subcategory of mod-Λ, which contains the projective modules. The main aim of this article is to prove that the resulting relative homological dimensions of modules are preserved by stable equivalences between Artin algebras. As a corollary, we see that Auslander’s notion of representation dimension is invariant under stable equivalence (a result recently obtained independently by Guo). We then apply these results to the syzygy functor for self-injective algebras of representation dimension three, where we bound the number of simple modules in terms of the number of indecomposable nonprojective summands of an Auslander generator.      

关于余挠三元组的余星子范畴和余倾斜子范畴

设$\mathcal{A}$ 是一个Abel范畴,且 $(\mathcal{X}, \mathcal{Z},\mathcal{Y})$ 是一个完全遗传余挠三元组.介绍 $\mathcal{A}$ 的 $n$-$\mathcal{Y}$-余倾斜子范畴的定义,并给出 $n$-$\mathcal{Y}$-余倾斜子范畴的一个刻画,类似于 $n$-余倾斜模的 Bazzoni 刻画.作为应用,证明了在一个几乎 Gorenstein 环 $R$ 上, 如果 $\mathcal{GP}$ 是 $n$-$\mathcal{GI}$-余倾斜的, 那么 $R$ 是一个 $n$-Gorenstein 环, 其中 $\mathcal{GP}$ 表示 Gorenstein 投射 $R$-模组成的子范畴且 $\mathcal{GI}$ 表示 Gorenstein 内射 $R$-模组成的子范畴. 进而, 研究 任意环$R$上的$n$-余星子范畴, 以及关于余挠三元组 $(\mathcal{P}, R$-Mod, $\mathcal{I})$ 的 $n$-$\mathcal{I}$-子范畴与 $n$-余星子范畴之间的关系, 其中 $\mathcal{P}$ 表示投射左 $R$-模组成的子范畴且 $\mathcal{I}$ 表示内射左 $R$-模组成的子范畴.     

倾斜RnA-模及其导出的挠理论

本文通过函子Ｔ＝－ＡＲｎＡ讨论了倾斜Ａ 模与倾斜ＲｎＡ 模的重要联系，推广了［１］的主要结果；讨论了倾斜ＲｎＡ 模ＴＸ与倾斜Ａ 模导出的挠理论在相同性和分裂性等方面的关系．     

Approximations and cotorsion pairs related to a tilting pair

The notion of a tilting pair Miyashita in 2001. It is a useful tool in cotorsion pairs related to a fixed tilting （covariantly） finite subcategory and a tilting pair were given in this paper. over artin algebras was introduced by the tilting theory. Approximations and pair were discussed. A eontravariantly eotorsion pair associated with a fixed     

Categories of exact sequences with projective middle terms

Let A be a finite-dimensional algebra over an algebraically closed field k,E the category of all exact sequences in A-mod,MP(respectively,MI)the full subcategory of E consisting of those objects with projective(respectively,injective)middle terms.It is proved that MP(respectively,MI)is contravariantly finite(respectively,covariantly finite)in E.As an application,it is shown that MP=MI is functorially finite and has Auslander-Reiten sequences provided A is selfinjective.     

Tensor Products of Torsion Free C n -Modules of Finite Degree and Finite Dimensional Modules

It is known that every torsion free C _n -module of finite degree is completely reducible. In this article, we provide a formula for the decomposition of the tensor product of a simple torsion free C _n -module of finite degree with a simple finite dimensional C _n -module. As a byproduct we obtain a recursion formula for the decomposition of the tensor product of any two simple finite dimensional C _n -modules.     

Equational Theories for Classes of Finite Semigroups

It is proved that there exists an infinite sequence of finitely based semigroup varieties such that, for all i, an equational theory for and for the class of all finite semigroups in is undecidable while an equational theory for and for the class of all finite semigroups in is decidable. An infinite sequence of finitely based semigroup varieties is constructed so that, for all i, an equational theory for and for the class of all finite semigroups in is decidable whicle an equational theory for and for the class of all finite semigroups in is not.     

Gorenstein子范畴与相对奇点范畴

令A是阿贝尔范畴, T是A的一个自正交子范畴, 且T中每个对象均有有限投射维数和内射维数. 假设左Gorenstein子范畴lG(T)等于T的右正交类,且右Gorenstein子范畴rG(T)等于T的左正交类,我们证明了Gorenstein子范畴$G(T)$等于T的左正交类与T的右正交类之交,并且证明了它们的稳定范畴三角等价于A关于T的相对奇点范畴.作为应用,令$R$是有有限左自内射维数的左诺特环, $_RC_s$是半对偶化双模,且所有内射左$R$-模的平坦维数的上确界有限, 我们证明了 若$\mbox{}_RC$有有限内射（平坦）维数且$C$的右正交类包含$R$,则存在从$C$-Gorenstein投射模与关于$C$的Bass类的交到关于$C$-投射模的相对奇点范畴间的三角等价,推广了某些经典的结果.     

有限变形弹性理论随机变量变分原理及有限元法

本文将材料、载荷、结构几何形状、力和位移边界条件的随机性,直接引入有限变形弹性理论的泛函变分表达式中,应用小参数摄动法,建立了统一的随机变量变分原理及非线性随机有限元法,并将其应用于结构可靠性分析。算例表明,应用此方法处理随机变量的力学问题,具有使程序实施简便,计算效率高等优点。