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Arad and Blau proved that an abelian table algebra can be viewed as a group algebra of some abelian group G. Chapter 3 of this paper gives the structural theorem of abelian table algebras by defining a group structure in table basis. Furthermore, the structure of elementary abelian table algebras is discussed using the number of composition series of table algebras.

Arad和Blau证明了abel表代数等价于某个有限生成abel群G的群代数，受此启发本文第3节通过定义表基的一个群结构给出了abel表代数的结构定理，并从合成列数目的角度对初等abel表代数进行了细致刻画。

Also prove that every bounded linear approximately local Hilbert space representation of a abelian von Neumann algebra is a representation,every bounded linear approximately 2- local Hilbert space representation of a von Neumann algebra is a representation.

同时证明了交换von Neumann代数的有界近似局部表示是表示，每个von Neumann代数的有界近似2—局部表示是表示。

Secondly, it has drawn out the pointed YD-Lie algebras definition, in the category of Yetter-Drinfeld modules, let Z be a torsion-free abelian group, if we have a symmetric braiding c, for each G-graded algebra V over the G-graded space, a new Lie superalgebra with an operation _c satisfying an actions, then we can obtain a new Lie superalgebra, this paper to call it pointed YD-Lie algebra.

其次引出了点YD-李代数，即：在Yetter-Drinfeld模范畴中，对任意的一个G-分次代数Z(G为无挠群V，引入对称辫子c后，在V内作_c运算，即可得到一种新的李代数(本文称之为点YD-李代数)。

Vector spaces are a central theme in modern mathematics ; thus, linear algebra is widely used in both abstract algebra and functional analysis .

向量空间的一个中心主题在现代数学，因此，线性代数被广泛使用在抽象代数和功能分析。

In addition to calculus with linear algebra, I had two semesters of mathematical analysis, partial differential equations, abstract algebra was also a senior this semester in the measurement theory.

除了微积分跟线性代数，我还上了两个学期的数学分析，偏微分方程，抽象代数还有在大四这个学期上的测量理论。

Mode of exquisite visual is a visual image thinking in comparison to understand some of the more abstract algebra problem for preliminary exploration mode, the purpose is to make the direct-viewing can better applied to high school algebra teaching

模式直观讲究的则是一种以比较直观形象的思维来理解一些较为抽象的代数问题，为此初步探索模式直观的目的在于使之能够更好地应用到中学代数教学之中。

I am a professor of the Department of Applied Mathematics at Xiamen University, a doctoral supervisor, and also the mentor of Mr. Ben Niu in the course Linear Algebra and the course Abstract Algebra. Therefore I have good knowledge of his academic capabilities and potential, so to speak...

我是厦门大学数学系教授、博士生导师，也是牛犇线性代数和抽象代数的授课老师，可以说我对他的学习能力和发展潜力是比较了解的，听说他正申请攻读贵校的硕士研究生课程，我当然全力支持。。。

This dissertation is changed into two parts. The first part, the theory and application about Wu-Ritt differential characteristic sequence method are discussed, which involves the theories of differential equations, abstract algebra and computer algebra etc.

本文共分两部分，第一部分讨论微分特征列法的理论和应用问题，涉及到微分方程，抽象代数，计算机代数等重要学科。

Higher algebra is an abstract and theoretical subject.In the teaching,it is hard to join the examples with the real life.This gives people the impression that learning algebra is not useful.

高等代数是一门抽象性和理论性较强的学科，在教学中所涉及的例子较少能与实际生活密切相连，让人感觉到学习的内容与生产实践脱节，体现不了数学的应用价值。

We explain the basic conception of the Lie group, Lie algebra and Riemannian manifolds in detail, deeply analyze and research the Special Euclidean Group SE(3) and se(3) in the Lie group, Lie algebra. Establish the relation between the adjoint transformation Adg and the operatorφ(k + 1,k) under a particular condition , substitute the operatorφ(k + 1,k)with spatial adjoint operator Ad kk ?

在多体系统动力学理论体系中，详细阐述了Lie群、Lie代数和Riemannian几何的基本概念，对Lie群、Lie代数中的特殊Euclidean群SE(3)和se(3)作深入分析与研究，建立Lie括号下的伴随变换Adg在特定条件下与空间算子代数理论中的空间变换算子φ(k + 1，k)之间的相互关系，并将空间伴随算子Ad kk ？

In the negative and interrogative forms, of course, this is identical to the non-emphatic forms.

。但是，在否定句或疑问句里，这种带有"do"的方法表达的效果却没有什么强调的意思。

Go down on one's knees;kneel down

屈膝跪下。。。下跪祈祷