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The main aim of this paper is to classify finite dimensional Hopf algebras, especially basic Hopf algebras.

本论文的主要目的是分类有限维的Hopf代数，特别地去分类有限维的基本Hopf代数。

By studying measure theory, the students are asked to understand σ-algebras, measure, measurable functions, integral, the measure theory of product spaces, Fubini theorem, and the representation theory of Boolean algebras.

通过本课程学习，使学生掌握σ-代数、测度、可测函数、积分，初步掌握乘积测度空间的构造及Fubini定理，以及布尔代数的表示理论。

The aim of this note is to develop the theory of corings and Galois theory for weak Hopf algebras, then we get some corresponding results about weak Hopf algebras.

弱Hopf模可以看成是一个上环上的余模，这就意味着Galois上环的一般理论能够运用于弱Hopf代数。

Moreover we describe the structure of Hopf algebroid by the motivating examples such as Weak Hopf algebras, groupoid algebras.

进一步从弱Hopf代数、群胚代数等具体例子中刻画Hopf代数胚的构造。

We use methods of the representation theory to prove that generalized Taft algebras are selfinjective Nakayama algebras, and provide their Gabriel quivers and relations, and determine all indecomposable representations.

我们利用表示论的方法，证明这类代数是自内射的Nakayama代数，给出其Garbriel箭图以及关系，并确定了它的所有不可分解表示。

Nest algebras are the natural generalizations of upper triangular matrix algebras in infinite dimensional spaces and an important object...

套代数是上三角矩阵代数在无穷维空间上的自然推广，是一类重要的非自伴算子代数。

Subsequently, we discuss the generalized derivable mappings at zero point on standard operator algebras and show that every generalized derivable mapping at zero point on standard operator algebras is a generalized inner derivation.

其次又对标准算子代数上的在零点广义可导的线性映射进行了讨论，证明了标准算子代数上的在零点广义可导的线性映射是广义内导子。

It is proved that an R-algebra isomorphism between two integral table algebras must be an integral table algebra isomorphism if it is compatible with the so-called normalizings of the integral table algebras.

我们证明了两个整表代数之间的一个R-代数同构必是一个整表代数同构只要它与一种标准化变换相容。

In chapter 2, we consider the isomorphisms of integral table algebras. For integral table algebras with integral table basis B we can consider integral R-algebra RB over a subring R of 〓, the ring of the algebraic integers.

第二章 我们考虑了有理整表代数间的同构问题：对任意整表基为B的整表代数，我们研究了代数整数环〓的一个子环R上的整R-代数RB。

The thesis studies several questions about integral table algebras and C-algebras.

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Liapunov—Schmidt method is one of the most important method in the bifurcation theory.

Liapunov—Schmidt方法是分叉理论的最重要方法之一。

Be courteous -- even when people are most discourteous to you .

要有礼貌──即使当別人对你最不礼貌的时候。