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We also can give the structure theorem for finite dimensional basic Hopf algebra of tame type in the radical graded case.

对于Tame型的Basic Hopf代数，我们可以给出的是根分次情形的结构定理。

The fact that a fuzzy ideal of a BCI algebra is closed if and only if it is a fuzzy subalgebra is proved.

证明了BCI代数的一个Fuzzy理想是闭的，当且仅当它是一个Fuzzy子代数。

There is a close relationship between a left L-comdule algebra A and its coinvariants subalgebra C.

注意到左L-余模代数A和它的余不变子代数C存在很密切的关联，我们称此关系是Morita关系。

So in a noncommutative mathrm C^*-algebra, there must exist a hereditarymathrm C^*-subalgebra which is not a closed ideal.

因此在非交换的 mathrm C^*-代数中必有一个非闭理想的遗传子代数。

Then we study the adjoint action of the quantum algebra u_qf(K, H and discuss the structure of its locally finite subalgebra.

讨论了量子代数U_qf(K，H上的伴随作用并给出了其局部有限子代数的结构定理。

Over a field of arbitrary characteristic, we construct a class of associative superalgebras of Weyl type and a class of Lie superalgebras of Weyl type from ∧(2, 2) and the polynomial algebra of the special deravation subalgebra of it. In addition, we prove that the sufficient and necessary conditions of the simplicity of the associative and the Lie superalgebras.

在任意特征域上，从∧(2，2)和它的特殊导子的子空间的多项式代数出发，构造了一类Weyl型结合超代数和一类Weyl型李超代数，进而给出并证明了它们为单的充要条件。

In chapter 1, we introduce the development of module theory and it s applications in the development of algebra,and present conditions of development of prime submodule s,prime radicals,isolated submodules.

本文讨论了环与模范畴中一个重要的子模类—孤立子模的一些性质以及它与强不可约子模等之间的一些联系，并引入了强孤立子模和局部孤立子模的概念，探讨了它们的一系列性质，在第一章中，介绍了模论的发展，模论在代数的发展中所起的重要作用以及素子模，素根和孤立子模的发展现状；在第二章中，给出了与本课题有关的重要概念及其结论。

And there is a natural graded G-algebra isomophism〓.3where Nis the subvariety of all the ad-nilpotent elements in the Lie algebraof G.

并且存在分次G-代数同构〓6这里N是G的Lie代数中的伴随幂零元全体。

It includes symbolic logic, set theory, graph theory and algebra system.

本课程主要包括数理逻辑、集合论、图论、代数系统四部分内容。

In section 2,we characterize the minimal ideals of finite dimensional symmetricself-dual Lie algebras over the complex field and gives an optimistic lower bound for thedimension of the space of invariant symmetric bilinear forms on a symmetric self-dualLie algebra by means of the number of linearly independent minimal ideals.

在第二节中，我们完全刻划了有限维对称自对偶李代数的极小理想；用线性无关极小理想的个数给出了一个对称自对偶李代数上由不变对称双线性型构成的线性空间维数的最好下界

Looking to bounce back from defeat against Cesena last weekend, the Calabrian boss will be sticking to his tried and tested 4-3-3, with Lopez and Sedivic joined up front in Giampaolo's absence by either Nanni or Plasmati.

鉴于上周末对切塞纳的比赛中反败为胜，这支南方球队将会更坚持其一贯而有效的4-3-3阵型，洛佩斯和塞德维奇将取代受伤缺席的詹保罗，和纳尼或者帕斯马蒂中的一个搭档锋线。

Meanwhile, their exposure to the more freewheeling ways of the West broadened dramatically.

另外，西方较自由的生活方式对年轻人的影响增大。