查询词典 ring of integers

According to algebraic number theory,all solutions of Pocklington equation in a ring of integers of a quadratic imaginary field are determined,which implies that the equation has only several solutions in the ring.

利用代数数论的理论与方法，决定了一个重要的不定方程在一个特殊的虚二次域整数环中的解，从而指出这个方程在比整数环更大的环中也仅有有限个解。

The pupose of the research is to develops public key encryption and digital signature shemes based on matrix canonical decomposition problem, or matrix diagonalization problem over Z/n, the ring of integers with modulo-n addition and multiplication in particular, where n is an RSA modulus.

本课题研究基于矩阵经典分解问题，特别是Z/n上矩阵对角化问题的公钥密码与数字签名算法，其中n是一个RSA模数。新算法采用由一个矩阵多项式构成的多维单向陷门函数，其单向性由矩阵对角分解问题(即通过相似变换将矩阵化为对角型的问题)的复杂性来保障，对该函数求逆的陷门由矩阵的特征值或特征向量提供。

In this paper, after the introduction of the basic concepts and the main results on K〓 theory, relative K〓 theory and the theory of classical groups of degree 2 which is related to K〓 theory, we study the problems of the computation of K〓 for the ring of integers of quadratic imaginary fields, examples of subrings of quadratic fields which are not universal for GE〓 and generating set of the Cokernel of the canonical homomorphism from K〓 to K〓.

本文在介绍了K〓理论和相对K〓理论以及与K〓理论有关的2阶典型群的基本概念及主要成果之后，对于虚二次域代数整环的K〓群的计算，非GE〓泛的虚二次域的子环以及K〓到K〓的自然同态的余核的生成元集等问题进行了研究。

A ring of integers derived from the set of all integers according to the following rule: Let N be an integer greater than 1, and A and B be two other integers; if N is a factor of A?

由全体整数的集合按下列规则产生的整数环：设N为大于1的整数，A和B是两个其它整数，若N是A？

A ring of integers derived from the set of all integers according to the following rule: Let N be an integer greater than 1, and A and B be two other integers; if N is a factor of A·B, then A is said to be congruent to a B modulo-N.

由全体整数的集合按下列规则产生的整数环：设N为大于1的整数，A和B是两个其它整数，若N是A·B的因子，则称A与B是模N的同余式。

In chapter 4, Based on the orthogonality relations and duality of C-algebras, we study the decompositions of C-algebras, and give a Fourier inversion formula on C-algebras, which generalizes the Fourier inversion formula on the center of a finite group algebra over complex. As an application, we characterize the integral closure of C-algebras over the ring of integers, and show a necessary and sufficitient condition for elements of C-algbras being algbraic integral over integers.

第四章 我们应用C-代数的正交性及对偶性刻画了C-代数的一个分解，给出了C-代数上这个完全分解的Fourier反演公式，从而推广了Z分解的Fourier反演公式；作为Fourier反演公式的一个应用，我们刻画了Z在整数环Z上的整闭包，进一步我们研究了C-代数在整数环Z上的整闭包，给出了C-代数在整数环Z上为整元的一个充要条件。

In chapter 2, we consider the isomorphisms of integral table algebras. For integral table algebras with integral table basis B we can consider integral R-algebra RB over a subring R of 〓, the ring of the algebraic integers.

第二章 我们考虑了有理整表代数间的同构问题：对任意整表基为B的整表代数，我们研究了代数整数环〓的一个子环R上的整R-代数RB。

Browkin and so on, an available method to get improved bounds for the norm of exceptional places in computing K〓 groups for the ring of integers in quadratic imaginary fields is obtained and as an application, K〓Z is determined.

Browkin等人工作的基础上，得到了估计虚二次域整环的K〓群的计算中例外位的范数的界的较有效的方法，并且作为应用，确定了K〓Z。

Through ordering the finite places by their principlal norm, much lower bounds for the norm of exceptional places in computing K〓 groups for the ring of integers in quadratic imaginary fields with class number 2 or 3 is obtained.

根据有限位的主范数将有限位进行排序，较大幅度地降低了类数为2或3的虚二次域整环的K〓群的计算中例外位的范数的界。

In vector algebra, addition are defined to add coordinates entries respectively,and this system of operation is the direct sum Z Z={|a,b are integers} of integers ring Z,the operations are+=,=.

向量代数加法就是这样按照分量加法在运算，再加上按照分量的乘法，这个运算体系就是整数环Z的直和Z Z={|a，b为整数}，其上的运算就是+=，=。

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。