交换群

The security~ of these cryptosystems is based on the dificulty in solving descrete logarithms with Abelian group .

本文讨论了一些公钥密码体制(ElGamal加密与解密算法、Diffie -Hellman密钥交换方案和Shamir协议)在阿贝尔群上的扩展，它们的安全性均建立在阿贝尔群上离散对数求解困难性的基础之

Semilattice graded weak Hopf algebra is a special case of weak Hopf algebra and a generalization of Hopf algebras, in Section 1.3, we will give results and applications to the Maschke's and Dual Maschke's Theorem of semilattice graded weak Hopf algebra.

尽管有限Clifford幺半群的量子偶确实是有限群量子偶的一个推广，但是[L2]中的量子偶一般情况下是不能够看作是Hopf代数量子偶的一个推广，这是因为我们在[L2]中要求所有讨论的弱Hopf代数都是交换的。

In this paper, we investigate some basic properties of the noncommuting graph associated with a finite group and their effects on the structure of the group.

本文主要研究了有限群的非交换图的一些基本性质及其对群结构的影响。

Among which theorem 1 and theorem 2 are similar to the controlled convergence theorem and Lukin theorem in Lebesgue integral Theory.

定义μ=|G|／|Irr|。得到了定理1 若G是非交换有限群2。首先得到具有这种性质的非Abel有限单群的完全分类定理。

The first part: Let μ be the ratio of the order of a non-abelian finite group G to the number of irreducible character of the group.

本文研究了非交换有限群G的不可约特征个数与群G结构之间的联系，由以下两个部分构成。

This paper has firstly defined the factor struture M/P of commutatiuely residual monoid M by its sub-monoid P, then we have studied its properties and given out some isomorphism theorem.

本文首先定义了交换剩余幺半群M相对于其子半群P的商结构M／P，然后研究了它的性质并给出了一些同构定理。

The influences of derivations and adjoint ideal semigroups of prime ring with characteristic 2 on the prime ring are discussed, and several sufficient conditions for the prime ring being communitive ring or S4-ring and some necessary conditions for a class of prime rings being communitive rings are obtained.

先给出了一个利用导子和理想来判断素环的可交换性结论的证明，然后讨论了特征为2的素环的导子和归联理想半群对这个素环的影响，得到了素环成为交换环或者S4-环的几个充分条件及一类素环成为交换环的必要条件。

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。

The second part: We study the connection between a non-abelian finite p-group G and the number of conjugacy class of it .

第二部分，我们建立了非交换有限p-群G与其共轭类个数之间的关系，并且得到了较小阶的p-群G与其共轭类个数之间一种更简洁的相互决定关系。

In this paper, we discuss effect algebra and related topics. The main results are the following:1. Effect algebra is a commutative algebraic structure. To get a non-commutative algebraic structure.we introduced the concepts of left difference and right difference, and we also introduced the concept of the Bi-difference sets, the concept of pseudo-difference poset, and proved that pseudo-difference poset is equivalent to pseudo-effect algebra.

效应代数描述的是具有交换性的量子系统，我们借助于差运算的思想研究了不可交换的量子逻辑结构，建立了左差、右差、伪差偏序集、双差集等概念，证明了伪差偏序集与伪效应代数等价，并得到了双差集的幺半群表示定理。

Plunder melds and run with this jewel!

掠夺melds和运行与此宝石！

My dream is to be a crazy growing tree and extend at the edge between the city and the forest.

此刻，也许正是在通往天国的路上，我体验着这白色的晕旋。