整数环

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。

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。

By using the Euclidean algorithm and invertible linear transformation over an integral ring, the solution of integral indeterminate equations of the first degree was investigated in theory, and its matrix solution based on the elementary matrix transformation was proposed.

用欧几里德算法和整数环上的可逆线性变换，从理论上对整数一次不定方程组的解进行了深入研究，提出了用矩阵的初等变换求解整数一次不定方程组的矩阵解法，并利用MATLAB数学软件开发了相应的计算机程序。

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。

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。

Finally, we generalize the p-adic expansion of an integer to the J-adic expansionof a polynomial in the ring Z.

最后，我们将整数环Z 上的p-adic 展开式推广到了整系数多项式环Z上的J-adic 展开式。

Here consists of two parts: quadratic residue code over integer ring modulo 16 residue class ring—Z〓 and integer ring modulo 2〓 residue class ring—Z〓.

讨论的内容分为两大部分：整数环模16剩余类环－－Z〓与整数环模2〓剩余类环－－Z〓上的二次剩余码。

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。