查询词典 algebra over k

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。

We give some examples of BiFrobenius algebras based on the extensions of algebras and coalgebras . Let H be a bialgebra of finite dimension . Then T= H⊕H* has an algebra structure and a coalgebra structure also . We discuss the properties of T , and get the necessary and sufficient condition for T to be a BiFrobenius algebra .

然后根据代数余代数的平凡扩张给出一类BiFrobenius代数的例子，设H是有限维双代数， T= H⊕H*既有代数结构也有余代数结构，研究T的性质，给出了T成为BiFrobenius代数的充要条件，即定理3.9。

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。

In the chapter two, we will recall some basic concepts and properties in commutative algebra and homological algebra.

在第二章中，作者介绍了交换代数和同调代数的一些基本概念和性质。

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

Further some equivalent conditions for a trivial algebra are given, and that the mapping which maps the subset of the universal to the maximal congruence that saturates the subset being a -homomorphism, being order preserving, being constant mapping, the algebra being trivial are equivalent is proved.

最后利用该同余给出了关于平凡代数的几个等价条件，证明了泛代数的子集到渗透该集的最大同余的映射为保序映射、该映射为-同态、该泛代数平凡等是等价的。

The study of lattice-valued propositional logic system based on lattice implication algebra.On the bases of previous study, by using the concepts and methods of T algebras we established the lattice-valued propositional logic system LP , whose truth values domain is a lattice implication algebra, and discussed systematically the semantical and syntactical properties of LP , proved the soundness theorem 、consistency theorem、deduction theorem and the decidability of validity of the system when the truth values lattice is finite. We also discussed the relationship between the α-theorem of some premise, say A, and the closed sets that contain A.

本文在前人研究工作的基础上，利用T代数的概念与方法，建立了真值取于格蕴涵代数的格值命题逻辑系统LP，对它的语义及语法性质进行了较系统的研究，得到了它的可靠性定理、协调性定理及演绎定理等，证明了值格有限时系统"有效性"的可判定性并讨论了某一前提A下的α定理与包含A的闭集之间的关系。

The algebra homomorphism and Riesz homomorphism can be deducible for each other under some circumstances in complex f -algebra.

文中具体讨论了在复f-代数中复Riesz同态与代数同态在一定条件下可互推的结果。

The shaping method of noncircular part and the tool holder's radial motion characters in noncircular turning process are discussed in detail in the thesis.

论文详细研究了非圆零件的成型方法和加工过程中刀架的径向运动规律。

I have not really liked him,I do not like his this kind of disposition.

我没有真的喜欢他，我不喜欢他的这种性格。