整数环

Suppose G is a finite group, then QG is a semisimple Q-algera, obviously ZG is a Z-order of QG,we denote the maximal Z-order by ?.If G is not abelian, it is not an easy thing to determine г; if G is an abelian group, then QG is isomorphic to the direct sum of a finite number of number fields, and r is the direct sum of these rings of algebraic integers of those number fields, but which elements of QG belong to r is not clear.

设G是一个有限群，那么QG是一个半单代数，ZG是QG的一个Z-序，设Γ是QG的一个极大Z-序，当G是一个非交换群时，Γ的求解是困难的问题；当G是一个交换群时，QG同构于有限多个数域的直和，Γ相应的就是各数域代数整数环的直和，但Γ具体是QG中那些元素不清楚。

Ber use the algebraic integer ring of quadratic cyclotomic field to construct block codes for coding two dimensional signals which are able to correct some error patterns.

uber利用二次分圆域的代数整数环构作了面向二维信号且具有代数译码算法的纠错码。

In this paper,similar canonical form of involutory matrix on integral number ring is given,and we prove that similar canonical form of involutory matrix is unique.

给出了整数环上对合矩阵的相似标准型，并证明了其唯一性。

Let n ≥ 4 be a fixed integer, R be a unital commutative ring of characteristic not 2, and D_n be a D_n-type classical Lie algebra over R.

假设n是一个大于等于4的整数，R是特征非2的有单位元的交换环，D_n是环R上的D_n型李代数，N是D_n的一个极大幂零子代数。

In this paper, new classes of linear block codes over finite fields of the algebraicinteger ring of quadratic number fields Qd~(1/2 modulo irreducible elements with norm p or p~2 are presented. These codes can correct one error which takes from the cyclic subgroup of the multiplicative group of the finite fields. The results presented in this paper extend the corresponding results of previous papers.

在处理适用于二维信号的线性分组码时，我们考虑类数为1的有理数域二次扩域Qd~(1/2的代数整数环，利用范数为p或p~2的不可约元构造有限域，给出剩余类域的一组完全陪集代表元系，从而构造出一类有限域上的线性分组码，当错误取值于有限域乘法群的一个循环子群时，所得到的适用于二维信号的线性分组码可以纠单个错，推广了文[14-16]的结果。

The similar canonical form of involutory matrix on integral number ring is given,and the unigue of similar canonical form of involutory matrix is proved in this paper.

给出了整数环 Z上对合矩阵的相似标准型，并证明了其唯一性。

It only takes quadratic bit complexity for the cryptosystem to perform an encryption/decryption operation.(6) A public-key cryptosystem is proposed by using a special combinatorial problem defined over the matrix ring. The security of the scheme is related to but not directly dependent upon the integer factorization problem.

6使用矩阵环上的一个特殊的组合问题构造了一个公钥加密算法，其安全性与整数分解问题有关，但并不直接依赖于整数分解问题，而是依赖于一类特殊的矩阵组合问题。

This invention provides compounds of Formula; wherein: R is a moiety selected from the group: and n is an integer of 1 or 2; R is selected from hydrogen, amino,-NRR, alkyl of 1 to 12 carbon atoms optionally substituted, aryl of 6, 10 or 14 carbon atoms optionally substituted, alkenyl of 2 to 12 carbon atoms optionally substituted, alkynyl of 2 to 12 carbon atoms optionally substituted, halogen, and a 5 to 10 membered heteroaryl ring optionally substituted, having 1 to 4 heteroatoms independently selected from N, O and S; R is selected from hydrogen, alkyl of 1 to 12 carbon atoms optionally substituted, aryl of 6, 10 or 14 carbon atoms optionally substituted, alkenyl of 2 to 12 carbon atoms optionally substituted, vinyl, alkynyl of 2 to 12 carbon atoms optionally substituted and halogen; R is H, alkyl of 1 to 12 carbon atoms optionally substituted, cycloalkyl of 3 to 8 carbon atoms, bicycloalkyl of 5 to 10 carbon atoms or aralkyl optionally substituted; R is OH or -OH; R and R are each independently H or alkyl of 1 to 12 carbon atoms or when optionally taken together with the nitrogen atom to which each is attached form a 3 to 8 membered saturated heterocyclyl ring; R is alkyl of 1 to 12 carbon atoms optionally substituted; or a tautomer or pharmaceutically acceptable salts thereof.

本发明提供式的化合物；其中：R 1 为选自基团和的部分；n为整数1或2；R 2 选自氢、氨基、-NR 6 R 7 、具有1到12个碳原子的视情况经取代的烷基、具有6个、10个或14个碳原子的视情况经取代的芳基、具有2到12个碳原子的视情况经取代的烯基、具有2到12个碳原子的视情况经取代的炔基、卤素和具有1到4个独立地选自N、O和S的杂原子的视情况经取代的5元到10元杂芳基环；R 3 选自氢、具有1到12个碳原子的视情况经取代的烷基、具有6个、10个或14个碳原子的视情况经取代的芳基、具有2到12个碳原子的视情况经取代的烯基、乙烯基、具有2到12个碳原子的视情况经取代的炔基和卤素；R 4 为H、具有1到12个碳原子的视情况经取代的烷基、具有3到8个碳原子的环烷基、具有5到10个碳原子的双环烷基或视情况经取代的芳烷基；R 5 为OH或-OH 8 ；R 6 和R 7 各自独立地为H或具有1到12个碳原子的烷基，或当视情况与其所连接的氮原子连接在一起时形成3元到8元饱和杂环基环；R 8 为具有1到12个碳原子的视情况经取代的烷基；或其互变异构体或医药学上可接受的盐。

Maximal Z-order ; relative K_1 group; excision; ring of algebraic integers.

基础科学，数学，代数、数论、组合理论极大z-序；相对K_1群；切割；代数整数环

In this paper, we introduce the concepts of the great common P-divisor, least common P-multiple of two distinct nonzero elements x, y in arbitrary unique factorization domain R, and denote them byp, and p respectively.

在本文中，作为通常的整数环Z上的最大公因子和最小公倍数的推广，我们在惟一分解整环R上定义了最大公P-因子和最小公P-倍元，分别记为_P和_P。

But we don't care about Battlegrounds.

但我们并不在乎沙场中的显露。

Ah! don't mention it, the butcher's shop is a horror.

啊！不用提了。提到肉，真是糟透了。