查询词典 algebras

The study of lattice implication algebras On the basis of previous results of lattice implication algebras, we firstly studied some properties of implication filters, prime implication filters, maximal implication filters and ultrafilters. Then we laid stress on the study of two kinds of relatively general lattice implication algebras, i. e. complete and atomic lattice implication algebra and injective lattice implication algebra.

关于格蕴涵代数的研究本文在已有的格蕴涵代数研究结果基础上，首先研究了格蕴涵代数中蕴涵滤子、素蕴涵滤子、极大蕴涵滤子和超滤等的性质和相互的关系，然后重点较系统地研究了两类覆盖面较广的格蕴涵代数：完备的且原子的格蕴涵代数和内射的格蕴涵代数。

The weyl algebras are important because some classical Lie algebras are equivalent to that of the Weyl type algebras.

因为李超代数在物理学中有着重要的作用，并且李超代数紧密的依赖于李代数。

Based on the outcome of Xu Yang and Qin Keyun about lattice implication algebra and lattice-valued prepositional logic LP with truth-value in a lattice implication algebra, the author studied the properties of lattice implication algebra and the α-automated reasoning method based on α-resolution principle of LP. The specific contents are as follows: The Study of Lattice Implication Algebra On the basis of previous results of lattice implication algebra, this part consists of the following three points: 1. Some properties of lattice implication algebra L were discussed, and some important results were given if L was a complete lattice implication algebra. 2. The properties of left idempotent elements of lattice implication algebras were discussed, and the conclusion that lattice implication algebra L was equals of the directed sum of the range and dual kernel of a left map constructed by a left idempotent element was proved. 3. The properties of the filters of lattice implication algebra were discussed, the theorem was shown that they satisfy the hypothetical syllogism and substitute theorem of the propositional logic. 4. The concept of weak niters of lattice implication algebras and their properties and structures are discussed. It is proved that all weak filters of a lattice implication algebra form a topology and the the implication isomorphism betweem two lattice implication algebras is a topological mapping between their topological spaces. The Study of α-automated reasoning method based on the lattice-valued propositional logic LP In this part, the author given an a-automated reasoning method based on the lattice-valued propositional logic LP.

本文基于徐扬和秦克云的关于格蕴涵代数和以格蕴涵代数为真值域的格值命题逻辑系统LP的研究工作，对格蕴涵代数以及格值命题逻辑系统LP中基于α-归结原理的自动推理方法进行了系统深入的研究，主要有以下两方面的研究成果：一、关于格蕴涵代数的研究 1、对格蕴涵代数的格论性质进行了研究，得到了当L为完备格蕴涵代数时，关于∨，∧，→运算的一些结果； 2、对格蕴涵代数的左幂等元进行了研究，证明了格蕴涵代数L可以分解为任何一个左幂等元所对应的左映射的像集合与其对偶核的直和； 3、对格蕴涵代数的滤子的性质进行了研究，证明了滤子的结构相似于逻辑学中的Hypothetical syllogism规则和替换定理； 4、给出了格蕴涵代数中弱滤子的概念，对弱滤子的性质个结构进行了研究，证明了格蕴涵代数的全体弱滤子构成一个拓扑结构，格蕴涵代数之间的蕴涵同构是相应的拓扑空间之间的拓扑映射。

The main idea of this thesis is to apply the quiver technique in the representation theory of algebras to the study of Hopf algebras and bi-Frobenius algebras.

本学位论文的主要思想是将代数表示论中的quiver方法应用于Hopf代数和双Frobenius代数的研究。

Its main goal is to explore information in the K-theory groups of the index C*-algebras, the Roe algebras C*, by using the large-scale geometrical structure of proper metric spaces, including noncompact complete Riemannian manifolds, finitely generated groups, etc., so as to establish connections among geometry, topology and analysis of the geometric spaces, and furthermore, to solve other relating problems, say, the Novikov conjecture, the Gromov-Lawson-Rosenberg conjecture on positive scalar curvature, the idempotent problem in the theory of C*-algebras.

粗几何上的指标理论是"非交换几何"领域九十年代以来发展起来的重要研究方向，它孕育于非紧流形上的指标理论，其主要目标是通过几何空间（如非紧完备黎曼流形、有限生成群等）的大尺度几何结构探索指标代数，即 Roe代数，的K-理论群的信息，从而建立几何空间的几何、拓扑与分析之间的联系，并应用于解决其他重要问题，如Novikov猜测、Gromov-Lawson-Rosenberg正标量曲率猜测、群C*-代数幂等元问题等。

On the fuzzy ideals and the ultraproduct of BCK-algebras;2. On the Fuzzy Ideals and Their Ultraproduct of MV-Algebras;3. Moreover, the ultraproduct lattice implication algebras and the fuzzy ultrapr.

另外 ，文中借助于超滤概念提出了格蕴涵代数簇的超积及格蕴涵代数中模糊子集的模糊超积，并进而研究了模糊滤子、模糊关联滤子及模糊子格蕴涵代数的相应性质。

At present time thesemaps have become important objectors and tools in studying operator algebras. Nestalgebras is a class of most importaut non-semisimple, non-prime and non-self adjointoperator algebras. Their finite dimensional models are upper triangular matrix algebras,but the infinite dimensional models are more complex.

本文在已有成果的基础上，研究了一些类型的算子代数上的Jordan可乘映射，Jordan-triple可乘映射，Lie-skew可乘映射，初等映射，Jordan-triple初等映射，Lie导子，Jordan导子，局部导子和局部同构及其刻画问题。

In the fifth chapter,we study dipolarizations in some quadratic Lie algebras.Inthe first section,we obtain some results on the classification of dipolarizations in gen-eral quadratic Lie algebras,and prove that there exist dipolarizations in the solvablequadratic Lie algebras whose Cartan subalgebras consist of semisimple elements.

第五章讨论了某些二次李代数的双极化，在第一节中，我们给出了二次李代数的双极化的一些分类结果；特别证明Cartan子代数是由半单元组成的二次李代数上存在双极化，第二节确定了四维扩张Heisenberg代数的所有双极化，在第三节中，我们构造了2n+2维扩张Heisenberg代数的六类双极化，我们发现两个不同于半单李代数情形的有趣事实：（1）在扩张Heisenberg代数上同时存在对称和非对称双极化；（2）对应于扩张Heisenberg代数的双极化的特征元有的是半单的有的是幂零的。

The notions of algebras of quotients and weak algebras of quotients for Lie color algebras are given.

利用经典环论中由环构造商环的方法，人们得到了李代数的商代数的概念。

In this paper, we characterize the multiplier algebras of JC-algebras by double centralizers , and study the relationship between multiplier algebra M of complex C*-algebra A and C*-algebra C* M(Asa generated by the multiplier algebra of JC-algebra Asa, the self-adjoint part of A, Finally, we study the extension of JB-algebras.

本文用双中心子刻画了JC代数的乘子代数，并且研究了复C*－代数的自伴部分的乘子代数生成的C*－代数与原C*－代数的乘子代数之间的关系，最后研究了JB代数的扩张。

If you are unfortunate enough to the lovelorn, please tell me, I will help you out, really, please contact me!

如果你不幸失恋了，请告诉我，我会帮助你摆脱困境，真的，请联系我啦！

China's plan to cut energy intensity by 20 percent and pollutant discharges by 10 percent between 2006 and 2010 is a case in point.

中国计划在2006年到2010间降低20%的能源强度和减少10%的主要污染物排放，就是一个这样的例子。