代数

Chapter three: Define fuzzy congruence relation of MTL-algebra, prove that fuzzy fiter and fuzzy congruence relation is a bijective function in MTL-algebra, quotient algebra induced by congruence relation still forms a MTL-algebra; Introduce the relation between some kinds of fiters and fuzzy filters maitained above in IMTL-algebra,i.e. BR_0 algebra, which is a MTL-algebra satisfied inversely odering and involutive relation.

第三章：定义了MTL-代数中的Fuzzy同余关系，证明了MTL-代数中Fuzzy滤子与Fuzzy同余关系是——对应的，由同余关系所诱导的商代数依然构成一个MTL-代数；介绍了在满足逆序对合对应的MTL-代数-IMTL-代数，即BR_0-代数中上述几中特殊滤子，Fuzzy滤子之间的关系。

Using the main result, we also obtain a simple criterion to check if a given mathrm C^*-algebra A is Abelian, that is, A is Abelian if and only for any two positive elements a, bin A, there is a'in A such that ab=ba'.

利用文中的主要结论，还得到了判断 mathrm C^*-代数 A 是交换一个简单条件，即 A 是交换的当且仅当对 A 中的任何两个正元 a， b 存在 a'in A 使得 ab=ba'。

I need your help with, you know, algebra.

我希望你帮我辅导一下，你知道的，代数。

Fuzzy logic is studied with algebraic tools in this paper. A kind of algebraic abstract of fuzzy logic, Implication Algebra on a partial ordered set, is given. The relations between Implication Algebra and other algebraic structures, such as MV-Algebra and Heyting Algebra etc., and the filter and the structure of Implication Algebra on a partial ordered set are studied.

本文的目的是使用代数工具对模糊逻辑进行研究，给出模糊逻辑的一类代数抽象，即偏序集上的蕴涵代数，研究偏序集上蕴涵代数与其它代数结构，如MV-代数，Heyting代数之间的关系，以及偏序集上蕴涵代数的滤子与其结构等。

We also show that thc linking C~*-algcbra of the TRO-univcrsal free product of two TRO\'s is~*-isomorphic to thc universal free product of the linking C~*-algcbras of thc two TRO\'s.In addition, inspircd by thc concept of full amalgamated frcc product of C~*-algebras, by using thc full amalgamated free product of thc linking C~*-algcbras of ternary rings of operators,we introduce the definition of TRO-full amalgamatcd free product,and give its construction,which is provcd to satisfy the univcrsal propcrty.

另外，受C~*-代数全融合自由积概念的启发，利用算子三元环的连接C~*-代数的全融合自由积，本章把全融合自由积的概念扩展到了算子三元环上，引入了算子三元环全融合自由积的定义，给出了它的一个构造，证明了这种构造(来源：ABC论文3b3b3b网www.abclunwen.com)的确具有"泛性质"，并且证明了两个算子三元环的TRO-全融合自由积的连接C~*-代数*-同构于这两个算子三元环的连接C~*-代数的全融合自由积。

C~*—algebra; Operator space; Ternary ring of operators; Universal free product; Full amalgamated free product; TRO—homomorphism;*—homomorphism

基础科学，数学，数学分析C~*-代数；算子空间；算子三元环；泛自由积；全融合自由积； TRO-同态；*-同态

Number theory function; Smarandache function; Mean value; Asymptotic formula

基础科学，数学，代数、数论、组合理论数论函数； Smarandache函数；均值；渐近公式

In Boolean algebra, an ''.

在布尔''。'代数'。

We shall have occasion to deal with geometry, both Euclidean and non-Euclidean, with arithmetic, algebra, analytic geometry, the theory of irrationals, set-theory, calculus of probability, and mathematical logic.

我们将与算术，代数，解析几何机会几何处理，包括欧几里德和非欧几里德，是无理的理论，集理论，概率演算，和数学逻辑。

Finite commutative group; Symmetric bicharacter; Lie color superalgebra ; Left color symmetric algebra ; Left color symmetric structure

基础科学，数学，代数、数论、组合理论有限交换群；对称双特征标；着色李超代数；左着色对称代数；左着色对称结构

In contrast to the ubiquitous rising-sun-with-rays military flag of the Japanese, Chinese banners and ensigns feature a range of designs.

与遍地都是的太阳军旗不同，中国人的旗帜和徽章设计得各式各样。

From their small corner of Feng's Guangzhou headquarters -- a jumble of pink leashes, squeezable rubber steaks, and plastic doggy Santas for Fido's stocking -- Soleil's designers come up with at least five new products a month.

从Feng 设在广州总部的产品展示柜台上可以看到，Soleil的设计师每月至少设计出5件新产品。