代数的

基本解释 (translations)

algebraic  ·  algebraical

与代数的相关的网络例句 [注：此内容来源于网络，仅供参考]

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。

All real simple Malcev algebra,are classified according to whether or not they have a compatible complex structure and simultaneously we give all the invariant bilinear forms by the killing form of the real simple Malcev algebra or the killing form of it s complexification .

研究实单Malcev代数上的不变双线性型，仿照李代数的情形给出实Malcev代数上的容许复结构、实Malcev代数的复化以及Malcev代数上的不变双线性型等概念，并通过对实单Malcev代数上容许复结构的讨论，将实单Malcev代数上的不变双线性型分为两种情形。

Then we study the typical property of theirs form the starting of nature and constitute of the two types of Lie algebra, and we calculated separately their dimension, center, commutator algebra, Killing type, Cartan subalgebra, structure formula, root system, and so on.

本文主要研究了两类典型的李代数即李代数so*(2n)和g*，首先介绍了一些李代数的基本知识，并且给出了这两类李代数的组成结构，然后从这两类李代数的本质构成出发，研究它们的一些典型性质，分别讨论了它们的维数，中心，换位子代数，Killing型，Cartan子代数，结构公式，根系等。

We give some examples of BiFrobenius algebras based on the extensions of algebras and coalgebras . Let H be a bialgebra of finite dimension . Then T= H⊕H* has an algebra structure and a coalgebra structure also . We discuss the properties of T , and get the necessary and sufficient condition for T to be a BiFrobenius algebra .

然后根据代数余代数的平凡扩张给出一类BiFrobenius代数的例子，设H是有限维双代数， T= H⊕H*既有代数结构也有余代数结构，研究T的性质，给出了T成为BiFrobenius代数的充要条件，即定理3.9。

Ringel has given and studied the N_0I-graded twisted coalgebra and Ringel-Hall algebra in the reference [1]. Subsequently, people found that there is an analogy between Ringel-Hall algebra and Hopf algebra, and then they introduced the concept of twisted Hopf algebras and bitwisted Hopf algebras, and worked on them.

Ringel在[1]中引入并研究了N_0I-分次扭的余代数和Ringel-Hall代数，后来人们发现Ringel-Hall代数有类似Hopf代数的结构，随后，扭Hopf代数、双扭Hopf代数先后被引入和研究。

In chapter 5, local derivations and local automorphisms of nest subalgebras in von Neumann algebras and local higher cohomology -local 2-cocycles are studied. It is proved that every weakly continuous local derivation, respectively, every weakly local automorphism, of nest subalgebra of a factor von Neumann algebra is a derivation, respectively, an automorphism. Every norm continuous local derivation, respectively, every norm local automorphism, of the nest subalgebra associated to a countable nest in a factor von Neumann algebra is a derivation, respectively, an automorphism. Moreover, it is answered Larson's question. Finally, it is shown that every local 2-cocycle of any von Neumann algebra is a 2-cocycle.

第五章研究von Neumann代数中套子代数的局部导子和局部同构以及von Neumann代数的高维局部映射—局部2-上循环，证明了因子von Neumann代数中套子代数的每一个局部强连续导子和局部强连续同构分别是导子和同构；可数套所对应的套子代数的每一个有界局部导子和有界局部同构分别是导子和同构；同时，部分回答了Larson所提的问题；最后，得到von Neumann代数的每一个局部2-上循环是2-上循环。

Libermann.The early researcheson this kind of manifolds were closely related to Physics and Mechanics.But since1991,S.Kaneyuki published his result on the algebraic condition for the existence ofinvariant〓structures on a coset space,Lie theory has played the most impor-tant role in the study of this kind of manifolds.In particular,dipolarizations in a Liealgebra are closely related to the homogeneous〓manifolds.Dipolarizationsin semisimple Lie algebras and the homogeneous〓manifolds associated withthese dipolarizations have been studied by S.Kaneyuki,Z.X.Hou and S.Q.Deng.Inthe partⅡ of this thesis we study the dipolarizations in some quadratic Lie algebrasand the homogeneous parakahler manifolds associated with these dipolarizations.

Libermann给出的，早期的有关类流形的研究与物理和力学密切相关，自从1991年金行壮二发表了陪集空间上存在不变仿凯勒结构的代数化结果后，李群及李代数理论在这类流形的研究中起着主要作用，特别地，李代数的双极化与这类流形密切相关，半单李代数的双极化的相关几何，金行壮二，候自新和邓少强等人已作了研究，二次李代数是比半单李代数更广且带有非退化不变双线性型的李代数，本文主要研究了二次代数的双极化及相关几何。

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 formal deductive systenm for Fuzzy propositional calculus, R0-algebras and BR0-algebras have been studied. The concepts of WBR0-algebras are proposed, the relationship between it and BR0-algebras has been investigated, the definition of basis BR0-algebras is simplified. Based on discussing the relationship between regular FI-algebras and regular residual lattice, the relationship between FI-algebras and basis R0-algebras has been investigated.

研究了王国俊教授建立的模糊命题演算的形式演绎系统L和与之在语义上相匹配的R0-代数以及吴洪博教授提出的基础R0-代数和基础L系统，提出了WBR0-代数的观点，讨论了它与BR0-代数的关系，简化了BR0-代数的定义，在讨论正则FI-代数与正则剩余格之间关系的基础上，讨论了BR0-代数与FI-代数的相互关系。

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。

与代数的相关的网络解释 [注：此内容来源于网络，仅供参考]

algebraic adjunction：代数的附加

algebraic 代数的 | algebraic adjunction 代数的附加 | algebraic affine variety 仿射代数集

algebraic algebra：代数的代数

algebraic affine variety 仿射代数集 | algebraic algebra 代数的代数 | algebraic branch point 代数分歧点

algebraic lie algebra：代数的李代数

algebraic irrational number 代数无理数 | algebraic lie algebra 代数的李代数 | algebraic logic of pocket calculator 袖珍计算机的代数逻辑

algebraic integer：代数的整数

algebraic homotopy 代数同伦 | algebraic integer 代数的整数 | algebraic linear programming 线性规划问题的代数解法

algebraic：代数的, 关于代数学的

algebraic zero | 代数零点 | algebraic | 代数的, 关于代数学的 | algebraically closed field | 代数闭域

analytic group of a Lie algebra：李代数的解析群

李代数的根|radical of a Lie algebra | 李代数的解析群|analytic group of a Lie algebra | 李代数的扩张|extension of a Lie algebra

regular element of a Lie algebra：李代数的正则元

李代数的诣零表示|nilrepresentation of a Lie algebra | 李代数的正则元|regular element of a Lie algebra | 李代数的秩|rank of a Lie algebra

different of a simple algebra：单代数的差积

单代数|simple algebra | 单代数的差积|different of a simple algebra | 单代数的判别式|discriminant of a simple algebra

singular element of a Lie algebra：李代数的奇异元

李代数的理想|ideal of a Lie algebra | 李代数的奇异元|singular element of a Lie algebra | 李代数的上同调|cohomology of Lie algebras

complexification of a Lie algebra：李代数的复化

李代数的表示|representations of a Lie algebra | 李代数的复化|complexification of a Lie algebra | 李代数的根|radical of a Lie algebra