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+=，=。

Singer Leona Lewis and former Led Zeppelin guitarist Jimmy Page emerged as the bus transformed into a grass-covered carnival float, and the pair combined for a rendition of "Whole Lotta Love".

歌手leona刘易斯和前率领的飞艇的吉他手吉米页出现巴士转化为基层所涵盖的嘉年华花车，和一双合并为一移交&整个lotta爱&。

This is Kate, and that's Erin.

这是凯特，那个是爱朗。