模范畴

Similar to [KV2], for a Dynkin-algebra A, we prove that there is a bijection between the bi-aisles in Db and thestrictly full triangulated subcategories of Db which are closed under direct sum-mands.

运用[KV2]中的技巧，对Dynkin型k-代数A的模范畴的有界导出范畴Db，我们证明了其上的双aisles与其上的严格的且关于直和项封闭的三角满子范畴存在着一一对应的关系。

Ringel realized positive parts of semisimple Lie algebras in the framework of Ringel-Hall algebras. The main result of this thesis is to build a geometric and topological model over triangulated categories such as derived categories and stable module categories of repetitive algebras. We defines a Lie bracket by Euler characteristics of constructible subsets and thus realizes infinite dimensional Lie algebras of various types with non-degenerated bilinear form.

本文的主要结果是在导出范畴和重复代数的稳定模范畴等三角范畴水平上建立相应的几何-拓扑模型，并利用相应可构集的欧拉示性数定义了一个Hall代数的交换子乘法，从而在三角范畴水平上实现了一大类无限维李代数的整体构造，并且这类李代数本质上都具有非退化的不变双线性型。

Leading to a new proofs, we show that the left Drinfeld Double D -module category is isomorphic to the category of the Yetter-Drinfeld modules.

并且通过新的证明方法，我们得出左Dinfeld DoubleD-模范畴同构于Yetter-Drinfeld模范畴。

Based on the methods and techniques of covering theory, the structure of module category of tame concealed algebra, one-point extension, vector space category, finite enlargement, degeneration theory, stable equivalence and combinatorial method, we will classify all of the three-point algebras with Gabriel quiver the system quiver Q according to representation type. We get the classification theorem: Let A=kQ/I be a three-point algebra given by the system quiver Q.

本文综合利用覆盖理论，tame concealed代数模范畴的结构，单点扩张，向量空间范畴，有限enlargement，退化理论，稳定等价以及组合的方法等多种方法和技巧，将所有由系统箭图Q给出的三点代数按表示型进行分类，得到如下分类定理：Q是系统箭图，I是kQ的一个admissible理想。

The injective rings play an important role in the study of rings and categories of modules . First , we introduce the notion of ann-injective rings and CT-injective modules .Second,we make an inquiry into a series of their properties.Third,we give the definition of homological dimension of CT-injective modules.At last,we give the definition of FGT rings which is the extension of cogenerator rings.

本文对环与模范畴中一重要的模类—内射模进行了延拓，引入了ann -自内射环以及CT -内射模的概念，探讨了它们一系列的性质，并定义了CT -内射模的同调维数，最后对余生成子环进行推广得到了FGT -环，讨论了它与CT -内射环的关系以及它的一些性质。

The latter is essentially derived from the geometric realization of Happels triangulated equivalence between stable module category of repetitive algebra and bounded derived category of finite dimensional algebra. In terms of this realization, we deduce that the Lie algebra realized by derived category of a finite dimensional algebra is isomorphic to the Lie algebra realized by stable module category of the corresponding repetitive algebra.

后者本质上是Happel关于重复代数的稳定模范畴和导出范畴的三角等价的一个几何实现及其应用，使用这种几何实现，我们可以证明在重复代数的稳定模范畴上定义的李代数同构于相应的导出范畴上实现的李代数。

Then we discuss comodule algebra on the Hopf algebroid. If L is finite generated as a left R-projective module, left L-comodule category is equivalent to the left L〓-module category.

然后讨论Hopf代数胚的余模代数，如果L是有限生成的左R-投射模，那么左L-余模范畴与左L〓-模范畴是等价的。

For detail,we studied the Incidence Algebra I defined by finite Partially Ordered Set X,and sheaf F based on the topology T_x defined by the partial order;By studying the relation between finite module category mod I and the sheaf category Sh_x A,we proved that they are equivalent.

特别的，对给定的有限偏序集X确定的Incidence代数Ⅰ，及由X的序关系定义的拓扑结构T_X上的层F，通过考查有限模范畴modⅠ与层范畴Sh_XA之间的关系，证明了Incidence代数上的模范畴与层范畴的等价性。

In chapter 1, we introduce the development of module theory and it s applications in the development of algebra,and present conditions of development of prime submodule s,prime radicals,isolated submodules.

本文讨论了环与模范畴中一个重要的子模类—孤立子模的一些性质以及它与强不可约子模等之间的一些联系，并引入了强孤立子模和局部孤立子模的概念，探讨了它们的一系列性质，在第一章中，介绍了模论的发展，模论在代数的发展中所起的重要作用以及素子模，素根和孤立子模的发展现状；在第二章中，给出了与本课题有关的重要概念及其结论。

In this dissertation,we concentrate on the homological properties of DG mod-ules over connected DG algebras and study various homological invariants.

本文以连通DG代数上的DG模范畴为研究对象，系统地研究了连通DG代数上的DG模的同调性质及各种同调不变量。

Means the parent directory, so this command means to execute "toolchain.sh," which is in the current directory.

代表父目录，所以这个命令就是执行当前目录下的"toolchain.sh"。

Yes,In fact,I'm on our city ream.

是的。事实上我是我们市队的。