抽象代数

运用抽象代数的知识对整系数多项式进行摸p约化处理，得到了整系数多项式在有理数域Q上不可约的4个新判别法。

In this paper , We apply the knowledge of abstract algebra to study integral polynomials that are simplified by module p and obtain four new irreducibility tests for integral polynomials .

结合抽象代数，组合数学，矩阵理论等知识，提出一种有限阿贝尔群上Jacket矩阵的构造方法，扩展了Jacket矩阵家族。

The combination of abstract algebra , combinatorial mathematics and the matrix theory knowledge , we propose a new construction of Jacket matrix based on finite Abelian group , which expand the Jacket matrix family .

目前APOS理论在国外比较盛行，已经在函数概念、抽象代数、离散数学、微积分等多方面领域得到广泛应用。

APOS theory relatively prevails abroad at present and it has already been widely used in many aspects , such as function concept , abstract algebra , dispersed mathematics , calculus .

抽象代数教学中的素质教育

Education for All-round Development in the Tuition of " Abstract Algebra "

抽象代数中循环群的研究

Research on the Circulated Group in the Abstract Algebra

正是非欧几何和抽象代数的出现，使得张量分析得以产生。

Tensor analysis creates on the basis of non-Euclidean geometry and abstract algebra appearance .

在后来20世纪的发展中，抽象代数观点占了主导地位。

In 20th century , the view of abstract algebra is in the dominant position .

用抽象代数的方法系统分析二元集上仅有的16种运算，指出这16种运算中只有异或运算和等值运算能对二元集构成群；

Sixteen algebraic operations which binary set has only are systematically analysed with abstract algebra mathods .

通过抽象代数知识，求出所有正多面体的旋转群。

Using the knowledge of abstract algebra , the rotation groups of the regular polyhedron are determined .

这是抽象代数领域。这里一个重要的概念是，向量，推广到向量空间，以及线性代数研究。

An important concept here is that of vectors , generalized to vector spaces , and studied in linear algebra .

以抽象代数为工具，探索了全样本依赖与全连接依赖之间的关系。

The relationship between the total template dependencies and the total join dependencies is probed into by means of abstract algebra .

本文的目的在于利用抽象代数结构来描述抽象数据类型并给出它的数学含义；

The goal of this paper is to specify abstract data type and provide its mathematical meaning by using algebra structure ;

介绍代数学的分支与内容，包括代数学、初等代数、高等代数、抽象代数。

This paper introduces the branches and content of algebra , including general algebra , elementary algebra , advanced algebra and abstract algebra .

另一方面，多元样条函数与基础数学的一些领域，如，抽象代数，代数几何，微分方程及组合数学等，亦有着密切关联。

Moreover , multivariate splines also have certain relations with pure mathematics , such as , abstract algebra , algebraic geometry combinatorics and so forth .

在文献[3]中，以线性变换广义逆的形式讨论了广义逆矩阵问题，用到的工具主要是张量概念及记号等抽象代数方法。这些工具比较生僻难懂，而且不便于直接应用。

In paper [ 3 ] , the generalized inverse matrix is defined by abstract algebra method , which is difficult to understand and to use .

其中群论作为抽象代数研究的一个重要分支起源于对代数方程的研究，它开辟了全新的研究领域。

As an important branch of abstract algebra , theory of groups originated in the research of algebraic equations . It opens a new field of research .

或许比这些新方法的引入更为引人注目的是抽象代数的公理化、概念化的方法以及其对整个数学学科的深远影响。

Perhaps even more striking than the advent of these ideas has been the acceptance of the axiomatic conceptual method of abstract algebra and its pervading influence throughout mathematics .

本文根据大型新闻资料计算机检索系统对中文检索语言的具体要求，对中文叙词表结构进行了分析，并以抽象代数为工具进行推导，给出了一种叙词表结构的形式化的描述方式。

The structure of Chinese thesauruses of a large Chinese information retrieval computer system is analyzed and a kind of formal description is presented through strictly inferring by using abstract algebra .

抽象代数是数学研究的一个重要方向，它以特定的代数结构，如群、环、域、模等为研究对象。

Abstract algebra is one of important direction of mathematical research . Object of abstract algebra is special structure such as groups , rings , fields , modules and so on .

实例证明，本方法可以和已有的抽象代数系统联系起来，从而为控制数据对象上的各种操作提供可靠的理论依据。

Through an example we can prove the probability of associating it with the existing algebraic system , and provide a reliable theoretical basis for controlling the various operations in data objects .

并对近世代数（吴品三）、抽象代数（徐诚浩）中有关模格维数几个定理证明的遗漏，作了某些补证。

The paper also gives some corrections to several theorems and their proofs about the dimension of the modular lattice ih the books " Modern Algebra " by Wu and " Abstract Algebra " by Xu .

提出以集合论为工具建立在抽象代数理论基础上的修正次优子集多项式回归法，对回归过程的主要内容进行了充分的数学描述和讨论，给出了一个重要的定理和推论。

This paper by means of set theory , presents a modified suboptimal subset polynomial regression algorithm based on abstract algebra . In the paper , most of contents for regression process are adequately described and discussed in mathematics , one important theorem and corollary are given .

另外，那些已经得到解决的难题，比如四平方数定理，极少有被“机械的规则”证明的，往往都是通过创造性推演，或者构建新的抽象代数概念。

Furthermore , the difficult problems which had been solved , such as Gauss 's Four Square Theorem , had rarely been proved by anything like a ' mechanical set of rules ' , but by the exercise of creative imagination , constructing new abstract algebraic concepts .

提出贯穿高等代数理论的三条主线。它们是：从具体的数学对象向抽象的代数系统的转变；

This article advances three main leads of higher algebra theory .

初一处于小学与初中的过渡阶段，学习内容由具体的数转向了抽象的代数，意味着要从形象思维过渡到抽象思维。

The first grade of junior school is the transition stage between elementary school and junior high school , so the learning content has been changed from the specific number to the abstract algebra , which means it needs a transition from thinking in images to abstract thinking .

Arad和Blau在1991年从有限群的不可约特征标和共轭类的积的分解中抽象出表代数的概念，它是一类满足特定条件的定义在复数域上的有限维交换结合代数。

Arad and Blau abstracted the concept of table algebras , which are a class of finite dimensional , associative and commutative algebras over the complex numbers with certain specified properties , from the decompositions of products of either irreducible characters or conjugacy classes of finite groups .

具迹抽象类型的代数语义与继承

Algebraic semantics and inheritance of an abstract class with trace

作为动态逻辑代数抽象的动态代数，可以细致刻划程序的性质.本文引入上下文无关无穷代数概念，借助此概念将递归特性引入到动态代数之中，提出了递归动态代数。

The infinite context-free algebra is introduced and the Recursive Dynamic Algebra , a Dynamic Algebra having recursive operation , is proposed .

首先给出一种基于抽象数据类型的代数规格说明语言AAA；

AAA , an algebraic specification language based on the abstract data type , is introduced first .

抽象数据类型的代数方法研究

Research of Abstract Data Type with Algebraic Method