代数

Associated it we define a root system. In a suitable condition we define a Lie algebra to realize this root system, namely, using an Euler cocycle given by intersection matrix, we define an infinitely dimensional vector space with the Lie operation becomes a Lie algebra.

在适当的条件之下，我们给出了该根系的一个李代数实现，即利用该相交矩阵确定的一个欧拉cocycle和根系，我们定义了一个无限维向量空间和李运算，并且证明了这个无限维向量空间在该李运算之下构成一个李代数。

"Applied algebra" introduce application of algebra in cryptography and coding theory.

应用代数主要内容是一些代数知识在密码学和编码学中的应用。

The main purpose of this thesis is to study the application of the representation theory in Hochschild homology and cohomology groups of algebras, Hopf algebras and quantum groups, which are very active branches at present.

本学位论文主要研究代数表示论在代数的Hochschild同调群和上同调群，Hopf代数和量子群这几个当今很活跃的数学分支中的应用。

In the representation theory of finite-dimensional algebras, combinatorial tools as quivers and their representations provide effective method in computing Hochschild homology and cohomology groups of finite-dimensional algebras.

代数表示论中的组合工具—箭图及其表示的发展和应用，为计算有限维代数的Hochschild同调群与上同调群提供了有效的方法。

First, we give the definition of Lie color superalgebras using the symmetric bicharacter on a finite commutative group, and also we introduce some fundamental notions about Lie color superalgebras.

首先根据有限交换群上对称双特征标的概念，给出着色李超代数的定义，并介绍关于着色李超代数的一些基本概念与基础知识。

Let n ≥ 4 be a fixed integer, R be a unital commutative ring of characteristic not 2, and D_n be a D_n-type classical Lie algebra over R.

假设n是一个大于等于4的整数，R是特征非2的有单位元的交换环，D_n是环R上的D_n型李代数，N是D_n的一个极大幂零子代数。

Moreover, similar to the corresponding results in [L8], we will finish the decomposition and semi-simplicity of G-quantum doubles of semilattice graded weak Hopf algebras under the condition of commutativity.

首先，我们通过弱Hopf代数的skew-对来构造了一种新的拟双交叉积，这种skew对是对Takeuchi Hopf代数对的一个推广。

Symmetry group is a connected compact Lie group, the system has also a fine cascade decomposition.

该章正是从这一角度出发，通过参数确定了线性控制系统的对称代数，而且构造出的对称代数其维数是最大的。

Chapter one: Provide the simple introduction to basic conceptions and properties used in the article about MTL-algebra; prove the set of all the filters form a complete distribution lattice in MTL-algebra; Discussion some property characteristics of Boolean filter, at the same time introduce the conceptions of positive implicative filter and obstinate filter, receive some properties of them, discuss the relation between the important filters and their equivalent condition.

第一章：对文章中用到的关于MTL-代数的基本概念和性质给出简单的介绍，证明了MTL代数中的全体滤子之集构成一个完备的分配格；讨论了布尔滤子的一些性质特征，同时引入和固执滤子的概念，得到它们的一些性质，探讨了几类重要滤子之间的关系。

High School: Algebra, Geometry, Advanced Algebra, Trigonometry, Pre-Calculus conics and limits

高中：代数，几何，高等代数，三角学，？圆锥和极限

And discuss some key point of integrated management system design, include hazard identification and risk assessment and risk control in the occupational health and safety management, the measure of satisfaction target of customer, the flawlessness of law system, the integration of the integrated management system and enterprise standardization system, unify lead institution and work orgnization, integreted internal audit and integrated management review.

同时，论述了一体化管理体系构建中的几个主要问题，包括职业健康安全管理中的危险源辨识、风险评价和风险控制、顾客满意度的科学监测、法律、法规体系的完善、一体化管理体系与企业标准化体系的有机结合、统一的领导机构和工作机构、一体化的内部审核和管理评审。

Deepwater Taranaki is investigated for its petroleum potential, using all available seismic data tied to shallow-water wells.

运用与浅水井相关的现有全部震波探测数据考察了深海区塔拉纳基盆地的油藏前景。