代数等价

Firstly,a involution on Universal Clifford algebra 〓 is introduced.then we equip a inner product and the corresponding two equivalent norms onUniversal Clifford algebra 〓,and then we prove that Universal Cliffordalgebra 〓 is a Banach algebra with one of the above norms,these resultsare very important for further study in this field.

第一，本文创造性地准确地给出了在少Clifford代数〓上的一个对合运算表示，由此，我们给出了在泛Clifford代数〓上的一个内积，然后给出了相应的在泛Clifford代数〓上的两个等价的范数，并证明了若在〓上赋予其中的一个范数，则〓是一个Banach代数，这为在泛Clifford分析中进一步开展工作奠定了初步的基础。

Let L and P be Lie color algebras and let M be a graded module over P, the crossed modules which make M as their kernal and P as their cokernal are considered. It is shown that under a suitable equivalent relation, there is a bijection between the set of the equivalent classes CML and the homogeneous components of degree zero of H~3.

从交叉模的定义出发，对于给定的Lie color代数L，P以及阶化P模M，考虑所有以M为核、以P为余核的L的交叉模，在这些交叉模之间定义了一个等价关系，由此得到交叉模的等价类集CML，证明了CML与三维上同调群H~3的零次齐次部分之间存在一一对应，从而可以利用三维上同调群对Lie color代数的交叉模进行分类。

The thesis consists of the followingmain results:the Cauchy's integral formula on certain distinguished boundaryfor LR regular functions with values in a universal Clifford algebra 〓,theCauchy's integral theorem,the mean value theorem,the maximum modulus the-orem.the Taylor's expansion,the Laurent's expansion and the residue theoremetc..

第一章叙述了泛Clifford代数基本理论，其中，我们首先准确而又富有创造性地给出了在泛Clifford代数〓上的一个对合运算表示，由此，我们给出了在泛Clifford代数〓上的一个内积，然后，我们借此给出了在泛Clifford代数〓上的相应的两个等价的范数，并证明了若在〓上赋予其中的一个范数，则〓是一个Banach代数。

The algebraic and coalgebraic methods in computer science is investigated in general, including its basic ideas, the categorical properties of algebras and coalgebras, initial algebra and final coalgebra, bisimulation and behavior equivalence, coalgebraic specifications, and coalgebraic logics.

对代数方法与共代数方法的基本概念、代数与共代数范畴的性质、初始代数与终结共代数、双模拟与行为等价、共代数规范以及共代数逻辑进行了比较全面和深入的研究。

Schauengurg[2] considered more general case and found necessary and sufficient conditions for the cosmash product coalgebra H Q to be a Hopf algebra with a Hopf subalgebra H and a weak projection !

Schauenburg在文献[2]中把Radford的研究加以推广，给出了使余smash积HQ为Hopf代数，H为HQ的子Hopf代数，且具有弱投射π：HQ→H(即π是左模余代数同态，且π|_H=id_H)的等价条件。

In the fourth chapter, using algebraic method, we prove that tubular mutations are auto equivalences of the derived category of a derived tubular algebra, and apply this method to the case of tame concealed algebras, which generalizes a result of Meltzer .

第四章我们用纯代数的方法证明：tubular mutation是tubular型标准代数的导出范畴的自等价，并把该方法应用到tame concealed代数，从而推广Meltzer的结果。

The latter is essentially derived from the geometric realization of Happels triangulated equivalence between stable module category of repetitive algebra and bounded derived category of finite dimensional algebra. In terms of this realization, we deduce that the Lie algebra realized by derived category of a finite dimensional algebra is isomorphic to the Lie algebra realized by stable module category of the corresponding repetitive algebra.

后者本质上是Happel关于重复代数的稳定模范畴和导出范畴的三角等价的一个几何实现及其应用，使用这种几何实现，我们可以证明在重复代数的稳定模范畴上定义的李代数同构于相应的导出范畴上实现的李代数。

Some other conditions which the implicative operator of a Implication Algebra should satisfied in a logic system are given. The relations between MV-Algebra and Distributive Implication Algebra, Implication Algebra with condition are gained.

对于偏序集上蕴涵代数中的蕴涵算子引入了一些逻辑条件，得到了偏序集上具有不同条件的蕴涵代数与MV-代数之间的关系，给出了偏序集上蕴涵代数与MV代数之间的几个等价定理。

The so-called AT-algebras are inductive limits of finite direct sums of matrices over the extension algeras of circle algebra by K, where K is the C~*— algebra of all compact operators on a separable infinite dimensional Hilbert space.

若V_*与V_*同构，且保持单位元等价类；T与T仿射同胚，且同构映射与同胚映射相容，则存在E与E′的同构导出上述同构和同胚，所谓AT-代数即为圆代数通过κ的本质酉扩张的矩阵代数的有限直和的归纳极限，这里κ为可分的无限维复Hilbert空间上的紧算子全体，不变量中的V*为三变元Abel半群，T为迹态空间，[1]为单位元所在的Murray-von Neumann等价类，r_E为连接映射。

Part II of this paper studies the structure of symmetric self-dual Lie algebras.

假设李代数g带有一个与Killing具有相同性质的型B，即具有双线性性，非退化性，对称性和不变性，由于这样的李代数g的伴随表示与它的余伴随表示等价，我们称李代数g为对称自对偶李代数，称型B为它上的一个不变数积。

However, as the name（read－only memory）implies, CD disks cannot be written onorchanged in any way.

然而，正如其名字所指出的那样，CD盘不能写，也不能用任何方式改变其内容。

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