Construction of new bornological quantum groups based on Galois objects

Let A be a bornological quantum group and R a bornological algebra. If R is an essential A-module, then there is a unique extension to M（A）-module with 1x = x. There is a one-to-one corresponding relationship between the actions of A and the coactions of . If R is a Galois object for A, then there exists a faithful δ-invariant functional on R. Moreover,the Galois objects also have modular properties such as algebraic quantum groups. By constructing the comultiplication Δ,counit ε, antipode S and invariant functional φ onR×R, R×R can be considered as a bornological quantum group.

环F_2+uF_2的Galois扩张上的迹码

环F2+uF2是介于环Z4与域F4之间的一种四元素环,因此分享了环Z4与域F4的一些好的性质,此环上的编码理论研究成为一个新的热点。该文给出了环F2+uF2的Galois扩张的相关理论,指出此Galois扩环的自同构群不同于Z4环上的Galois扩环的自同构群;定义了Galois扩环上的迹码的概念及子环子码的概念,证明了此Galois扩环上的一个码的对偶码的迹码是该环的子环子码的对偶码。

格序群扭类与半单类之间的Galois联络

建立了格序群扭类与半单类之间的一种重要联系Galois联络 ,利用这种联系研究了极扭类的存在性并且给出了极扭类的一种表示 ,推广了格序群扭类的基本定理 .

域Q(a^(1/s))上方程f(x)=0的Galois群

重点讨论Q(a～(1/s))域上的方程f(x)=0的Galois群的计算.给出并且证明了命题:域Q(a～(1/s))上f(x)=0的Galois群是f(x)=0在Q上的Galois群的子群,特别如果f(x)不含xS-a的因子,即f(x)的系数中没有sa的某个组合,则f(x)在Q(a～(1/s))的Galois群与f(x)在Q上的Galois群等同.并用具体实例来展示命题的实际意义.

群余分次乘子Hopf代数的Galois对象(英文)

在这篇文章中,我们首先介绍群余分次乘子Hopf代数Galois对象的定义,然后给出通过交叉作用π来构造群余分次乘子Hopf代数Galois对象的方法.设G是群,(,Δ)是G-余分次代数量子群(A,△)的变形.若(X,α)是(A,△)的左Galois对象,定义α_(p,q):X_(pq)→M(pX_q),α_(p,q)=(πqi)α_q^(-1)p^(-1)q,q^(-1),则(X,α)是变形(,Δ)的左Galois对象,其中X_p=X_(p^(-1)),_q=A_(q^(-1)).同时,我们也研究了Galois对象的一些性质.

二元外代数的Z_2×Z_2-Galois覆盖代数的Hochschild(上)同调群

设∧是特征不整除4的域k上的二元外代数，五是以的Z2×Z2-Galois覆盖代数．利用组合的方法，覆盖代数∧的各阶Hochschild（上）同调群的维数被清晰地计算，并且在域k的特征为零时，五的各阶循环同调群的维数也被给出．

分裂域∑上Galois群的构造

针对具体的分裂域,方程的Galois群的结构是可以构造的.文中给出了构造方法和重要推论,通过具体的若干实例展示了方程的Galois群计算方法.

环上典型群及其在Galois环上矩阵集合分类上的应用

简述了近期环上典型群及其应用的主要研究情况,论述了环上典型群在矩阵分类研究上的应用.

有限维Galois扩张中正规闭包的一个性质

Galois扩张即正规可分扩张,是Galois理论中的基石.本文主要利用Galois理论讨论了有限维Galois扩张中的中间域,给出了有限维Galois扩张中中间域的正规闭包的一个性质。

特殊Galois环上矩阵Kronecker积的广义逆

利用环上矩阵理论,研究了Galois环R=Z／P^kZ上矩阵Kronccker积的广义逆,得到了环R上的矩阵Kronecker积的广义逆的一些性质及其存在的充要条件和等价条件。

A RECOGNITION OF SIMPLE GROUPS PSL(3,q) BY THEIR ELEMENT ORDERS

For any group G, denote byπe(G) the set of orders of elements in G. Given a finite group G, let h(πe (G)) be the number of isomorphism classes of finite groups with the same set πe(G) of element orders. A group G is called k-recognizable if h(πe(G)) = k <∞, otherwise G is called non-recognizable. Also a 1-recognizable group is called a recognizable (or characterizable) group. In this paper the authors show that the simple groups PSL(3,q), where 3 < q≡±2 (mod 5) and (6, (q-1)/2) = 1, are recognizable.

Two Important Classes of p-groups and the Orders of Their Automorphism Groups

In the paper we obtain two infinite classes of p-groups, calculate the orders of their automorphism groups and correct a mistake（perhaps misprinted） of Rodney James＇ paper in 1980.

Three-dimensionally ordered macroporous cross-linked polystyrene incorporating functional group via hydrophilic spacer arm

A versatile and effective method for incorporating functional groups on the pore wall of three-dimensionally ordered macroporous cross-linked polystyrene（3DOM CLPS） by hydrophilic spacer arm has been investigated.The 3DOM CLPS with pore size 865 nm was prepared by sacrifice template method.The hydrophilic spacer arm（polyethylene glycol,molecular weight is 600） was grafted to the 3DOM CLPS via nucleophilic substitution reaction.The other side of active hydroxyl can be further converted into a lot of other functional groups.In this report,the chelating ligand 2-mercaptobenzothiazole（MBZ） group was introduced on the end of the PGE chain to evidence the versatile functionalization approach.The functionalized ordered macroporous materials were characterized by FT-IR,element analyzer,SEM.The results reveal that the pores were successfully bonded with 2-mercaptobenzothiazole groups via hydrophilic spacer arms and the original morphology of ordered macroporous materials were remained after functionalization.The MBZ group density is 0.052 mmol/m^2.The functionalized 3DOM CLPS are expected to application as heavy metal ions adsorbent.

A study on distributive and modular lattice ordered fuzzy soft group and its duality

Soft set theory has a rich potential application in several fields. A soft group is a parameterized family of subgroups and a fuzzy soft group is a parameterized family of fuzzy subgroups. The concept of fuzzy soft group is the generalization of soft group. Abdulkadir Aygunoglu and Halis Aygun introduced the notion of fuzzy soft groups in 2009[1]. In this paper, the concept of lattice ordered fuzzy soft groups and its duality has been introduced. Then distributive and modular lattice ordered fuzzy soft groups are analysed. The objective of this paper is to study the lattice theory over the collection of fuzzy soft group in a parametric manner. Some pertinent properties have been analysed and hence established duality principle.

Galois序闭域上四元数体上矩阵的特征值问题

讨论了Galois序闭域上四元数矩阵的左(右)特征值的性质与计算问题,并给出了具体的计算实例.

Orders of Automorphism Groups of the p^6 Groups of Family Φ_(24)

Using the metabelian property, regularity, p-commutativity and some properties of congruence, this paper gave the orders of automorphism groups of family Ф24, which are the groups of order p^6 determined by Rodney James, where p denotes an odd prime.

Orders of Automorphism Groups of Some p-Groups

The orders of automorphism groups of the groups of order p^6 in the twelve family Ф12 axe produced, where p is an odd prime. Every group is analysed by utilizing the properties of metabelian, regularity and p-commutativity of finite p-groups, and the structure of the generators of its automorphism groups is obtained. Then the orders of automorphism groups are determined through some properties of equivalence in number theory.

Asymmetric Key Cryptosystem for Image Encryption by Elliptic Curve over Galois Field GF(2^(n))

Protecting the integrity and secrecy of digital data transmitted through the internet is a growing problem.In this paper,we introduce an asymmetric key algorithm for specifically processing images with larger bit values.To overcome the separate flaws of elliptic curve cryptography(ECC)and the Hill cipher(HC),we present an approach to picture encryption by combining these two encryption approaches.In addition,to strengthen our scheme,the group laws are defined over the rational points of a given elliptic curve(EC)over a Galois field(GF).The exclusive-or(XOR)function is used instead of matrix multiplication to encrypt and decrypt the data which also refutes the need for the inverse of the key matrix.By integrating the inverse function on the pixels of the image,we have improved system security and have a wider key space.Furthermore,through comprehensive analysis of the proposed scheme with different available analyses and standard attacks,it is confirmed that our proposed scheme provides improved speed,security,and efficiency.

The Class of Orderable Groups Is a Quasi-Variety with Undecidable Theory

Let G be a group. G is right-orderable provided it admits a total order ≤ satisfying hg1 ≤ hg2 whenever g1 ≤ g2. G is orderable provided it admits a total order ≤ satisfying both: hg1 ≤ hg2 whenever g1 ≤ g2 and g1h ≤ g2h whenever g1 ≤ g2. A classical result shows that free groups are orderable. In this paper, we prove that left-orderable groups and orderable groups are quasivarieties of groups both with undecidable theory. For orderable groups, we find an explicit set of universal axioms.

带内Galois群的Galois扩张

本文在Azumaya代数的条件下,对一般的带内Galois群的Galois扩张的结构进行了刻划。