模的范畴

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。

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。

It is well known that, determining the damage parameters from modal parameter shifts belongs to the group of inverse problems of dynamics.

根据结构模态参数来确定结构损伤情况，理论上属于动力学反问题的范畴。

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。

I am sure after a few weeks of adaptation and familiarization I will have no difficulty in functioning on a daily basis in an English speaking society or in participating fully in graduate studies.

在大学的三年的学习生活不仅给予我自身的充实，更重要的是磨练和培养了我较强的自觉能力和严谨，踏实的作风以及不怕困难的精神，对未来充满了信心！

As the first volcanoes erupted, one of the gases that bellowed out was steam.

在第一批火山喷发时，喷出的气体之一就是水蒸汽。