整环

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。

Using the presentation, suppose that M is the maximal ideal of a commutative local domain R and R/M=F〓 is a finite field with q elements, a generating set of elements at most is obtained for K=Coker K〓

设M为交换局部整环R中极大理想，R/M〓F〓为q元有限域，由这个表现得到了K=Coker的一个至多含有个元素的生成元集。

In this paper, we generalize Gr〓bner bases theory to quotients of principal ideal domains and R/-algebras.

本文将Gr〓bner基推广到/J上及一类R/-代数上，R是主理想整环，p是素元，I≠0。

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。

This paper studies the invariant, which is the linear preserving problem based on generalized inverse of matrices. The generalized inverse of matrices and the research status of preserving problems of generalized inverse are outlined. In the basis of deeply understanding the basic knowledge of linear maps, the definition, characteristics of generalized inverse and decomposition of matrix, the author analyzes the decomposition form of preserving idempotence and preserving tripotence in the PID, then studies on the linear maps form of preserving group inverses of symmetric matrices.

本文研究的不变量是矩阵广义逆线性算子的保持问题，概述了广义逆矩阵，广义逆保持问题的研究现状，在对线性映射的基础知识，广义逆矩阵的定义、性质和矩阵的分解深入理解的基础上，深入分析了保幂等、保立方幂等矩阵在主理想整环上的分解形式，继而研究了保对称矩阵群逆的线性算子形式。

The w-radicals of cyclic submodules of finitely generated free modules over unique factorization domains are discussed.

C中有限生成子群的一条离散准则。11。讨论了唯一分解整环中有限生成自由模的循环子模的w-根。

In chaper 2, first we prove that the simple associative algebras A are noncommutative domains.

在本文的第二章，我们首先证明单结合代数A为非交换整环。

The aim of this Paper is to explore the possibility of teaching polynomials in junior middle schools and the best method to teachthem.

本文主要研究在中学低年级用整环的观点讲授多项式理论的可能性，探索一种学生所能接受的教学方法。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。