查询词典 involutory algebra

Based on the filtered Lie algebra of the universal enveloping algebra, the algebraic structure of projected subsystems are studied. It is proved that they have simple decompositions, and the construction of the representations is given as well as the corresponding criterion for project limit controllability.

基于泛包络代数的滤李代数结构，研究了投影子系统的代数结构，证明它们具有简单的分解形式，并给出了它们的表示的构造方法和投影极限能控性的判别定理。

Lattice implication algebra is an algebraic system combinating lattice with implication algebra.

格蕴涵代数是徐扬教授为研究格值逻辑把格与蕴涵代数相结合提出的一个代数系统。

Linear Algebra is mainly a subject which studies the linear structure of finite dimensional linear space and its linear transformation while linear concept is in itself from the old Euclid Geometry. The concept of "Linear Space" is a kind of algebraic abstract. In many fields of modern engineering project and technology, because of the influence of computer and graph showing, the algebraic disposal of geometric questions, the visual disposal of algebraic questions, algebra and geometry are tightly combined.

线性代数主要是研究有限维线性空间及其线性变换这一代数结构的学科，而线性概念究其根源则是来自古老的Euclid几何，线性空间概念是几何空间的一种代数抽象，在现代工程技术的许多领域里，由于计算机及图形显示的强大威力，几何问题的代数化处理，代数问题的可视化处理，把代数与几何更加紧密地结合在一起。

Lattice implication algebra is a kind of algebraic structure combined with lattice and implication algebra. It is an important method in the research of lattice-valued logic.

格蕴涵代数是将格与蕴涵代数结合起来的一种代数结构，是研究格值逻辑系统及其性质的一个重要途径。

It is shown that, any reprersentation finite special biserial algebra has a Groebner basis theory, and a finite-dimensional basic algebra over an algebraically closed field is representation finite if and only if every module over it has a right Groebner basis theory.

证明了表示有限特殊双列代数有Groebner基，从而扩大了Groebner基理论的应用范围；证明了一个代数封闭域上的有限维代数是表示有限特殊双列代数当且仅当其上每个右模都有右Groebner基理论，从而扩大了右Groebner基理论的应用范围。

From the famous Gabriel's theorem ,a basic connected finite dimensional associative algebra A over an algebraically closed field can be looked as a quotient of a path algebra decided by a connected finite quiver Q.

由Gabriel 定理，代数闭域上基的，连通的有限维结合代数A 同构于一个由连通有限箭图Q 确定的路代数的商代数。

If one of the following conditions is satisfied , then the trivial extension T of H is not a bialgebra .(1) H is not a Hopf algebra ,(2) H is a Hopf algebra , but the antipode of H is not the identity map .(3) char can not divide 2dim H .

若下述三个条件之一成立，则T不是双代数：(1) H不是Hopf代数，(2) H是Hopf代数，但其反极元S不是恒等映射，(3) char不能整除2dim H。

We investigate the centralizer of an arbitrary element of a Lie algebra of type L and obtain a sufficient condition for a Lie algebra of type L being semisimple.

在李代数方面，我们研究了L-型李代数中任一元素的中心化子，给出了L-型代数为半单代数的充分条件。

The representations of the associative algebra A play an important role in the study of the representations of the vertex algebra.

践行"三个代表"重要思想，推动高校办公室管理创新6。结合代数A的表示与顶点代数的表示密切相关。

As a branch of modern algebra , finite fields is an abstract system in algebra which satisfies operational laws such as associative law, commutative law, distributive law etc.

作为近世代数学的一个分支，有限域是一个拥有传统算术四则运算的抽象代数系统，它满足结合律、交换律、分配律、消去律等运算法则。

Nowadays, most of research are to build a transmutative Petri Nets through adding controlling place sets, controlling arc sets and controlling policy to the basic Petri Nets, while the Controlled Petri Nets could be used to argue many controlling theory problems conveniently and to induce many logically and physically supervisory and solve the Event Feedback Controlling Problems and State Feedback Controlling Problem in DEDS supervisory theory.

目前大多数的研究表现为在变形后的受控Petri网基础上，利用各种方法求得各种逻辑型、结构型控制器，解决DEDS监控理论中的事件反馈控制问题与状态反馈控制问题。

On one hand, there are discussions with the works council and union about extension of short time working up to the end of September.

一方面，有讨论，工程理事会和联盟关于延长工作时间短至9月底。