代数扩张

Prime ideal decomposition is an important problem in algebraic number theory and is relative closely with the class field theory and so on.

素理想分解问题是代数数论中的一个重要课题，它与类域论的关系极为密切，因而如何判断K的素理想在K的有限扩张中的分解状况是一个十分有意义的问题。

At first, we give someelementary conception and properties of Novikov-Poisson Algebras, we elaborate on thegeneral conclusions about central extension and universal central extension in thechapter three.

我们首先给出了Novikov-Poisson代数的一些基本概念和性质，在第三章中详尽地阐述了中心扩张和泛中心扩张的一般结论。

Therefore, for every perfect Lie algebra L(E_1,E_2,E_3) with v = 2, its uniersal central extension has the vertex operator represention.

于是，对于每一个perfect李代数L(E_1，E_2，E_3)，当v=2时它的泛中心扩张都存在顶点算子表示。

Major results, such as the Sz.-Nagy Dilation Theorem, the Weyl-von Neumann-Berg Theorem and the classification of von Neumann algebras, are covered, as is a treatment of Fredholm theory.

主要成果，如Sz。，纳吉扩张定理，外尔，冯诺依曼，伯格定理与冯诺伊曼代数的分类，覆盖，就像一个Fredholm算子理论的待遇。

As we know, the resulting algebraic equations are large systems of non-linear equations with the expanded mixed finite element method for the equation.

用扩张混合有限元方法对其进行离散是常用的方法，其离散化所获得的代数方程组是一很大的非线性方程组。

In this paper,based on the discussion on isomorphisms,the Verma modules of Svir are studied,and the irreducibility of these modules are obtained.

对域 F 的加法子群 M以及α∈F，且 2α∈M ，苏育才及赵开明定义了 2类广义Virasoro超代数，它们分别被记成SVir和SVir，后者是前者的平凡扩张。基于对同构的讨论，研究了SVir的Verma模，并且得到了这些模的不可约性

Nilpotency of a table algebra depends on that of their table subsets and quotient subsets, which is not fully corresponding to extension problems of nilpotent groups.

同时会发现该条件在表代数幂零性的判别方面并不完全对应于幂零群的中心扩张。

II, Polynomial rings on a general field( on contrast of those over a number field): concepts of ring, ideals, field and several special rings as domains, principal ideal domains and unique factorization domains, the unique factorization theory of polynomial rings.

二、一般域上的多项式理论（是数域上多项式理论的推广）：学习环、域和几类特殊结构的环（整环、主理想环，唯一分解环等）的概念，多项式环的唯一分解定理；三、线性代数：讲述一般数域上的向量空间理论（是数域上向量空间理论的继续和推广），模的概念，主理想环上的模的结构及其线性变换的若当标准型等；四、一元多项式的解及域论：学习域扩张及其相关概念，伽罗瓦理论，用伽罗瓦定理判断根式解的存在性。

In Chapter 2, starting from a generalization of Hensel's Lemma to non-commutative case, we introduce the Brauer characters and the generalized decomposition numbers, and construct a kind of maximal semisimple algebras; then, similarly to Puig's methods, we prove Brauer's Second Main Theorem over arbitrary fields; applying it to blocks with nilpotent coefficient extensions, a formula on characters of such blocks is given; the formula of characters of nilpotent blocks is just an easy consequence of the fomula.

在第二章中，我们将Hensel的引理推广到非交换的情况，以此为起点，定义了Brauer特征标和广义分解数，构造了一类极大的半单的代数，类似于Puig的方法，给出了任意域上Brauer的第二主要定理；作为该定理的应用，我们给出了具有幂零系数扩张的块的特征标公式，幂零块的特征标公式只是它的一个简单的推论。

We give also a complete description on non-solvable symmetric self-dual Lie algebrasusing the language of double extension.

我们也用双扩张的语言给出了非可解对称自对偶李代数的一个完整刻划。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。