环论

用环论的方法证明了群分次环上的双积对偶定理，主要结果是当G为有限群时，R＃kG＃。

In this paper , using some techniques from ring theory , duality theorems for group-graded rings in double products are proved . The main result is that when G is finite , R # kG # .

环论作为一门重要的代数学科，它是代数几何和代数数论的基础。

As an important algebraic subject , Ring theory is the base of Algebraic Geometry and Algebraic Number Theory .

推广了环论中著名的Goldie定理。

So the famous Goldie 's theorem in Rings Theory is generalized .

最后讨论了在某些链条件下的幂零性，把环论中著名的Hopkins定理与Levitzki定理推广到双群结合环。

Finally , the nilpotency of two-group associative rings under certain chain conditions is studied by extending the classical Hopkins theorem and Levitzki theorem to these rings .

广义多项式恒等式（GPI）理论是环论的一个重要分支，对素环，半素环上各类型恒等式的研究是GPI理论发展的基础。

Ring theory contains generalized polynomial identity ( GPI ) theory as an important area , which is based upon the investigation of many special identities in prime and semiprime rings .

本文把环论中相应的构造性定理推广到双群结合环，并得到：环（А，Γ）的Koethe根是具某性质的素理想的交；

In this paper , the construction theories of rings are generalized to two-group associative rings . Thus , we have : Koethe radical of the ring ( A ,Γ) is the intersection of some prime ideals with a certain property ;

现如今，环论已经涉及到其他学科。

Now , the theory of rings has been related to other subjects .

自激振动理论问题归结为极限环论的研究。

Theory of self-excited vibration belongs to the study on the theory of limit cycles .

集成随机置乱和环论的图形图像公钥加密技术

Public Key Cryptosystem for Graphics and Image Based on Integrating Random Scrambling Permutation and Ring Theory

它的精确定义是用环论的语言来给出。这种定义非常抽象而且难以验证。

The accurate definition is given by the language of rings [ 9,42 ] , which is very abstract and is hard to verify .

关于单侧理想的结果在环论中是重要的，本文以左理想为对象，对左理想所含的相关理想及左理想的诣零幂零性进行研究。

The author takes left ideals as objects in this paper and does some research on relative ideals and the nil-nilpotence problem of left ideals .

借助环论与半群理论的思想方法通过对半环的子半环的条件进行加强，提出了半环的弱伪理想的概念。

By using method of ring and semi-group theory and by widening the satisfactory conditions of the subsemiring of semiring , the concept of weak pseudo ideal of semiring is introduced .

在计数组合学中，我们需要群论，环论，代数等理论。

In enumerative combinatorics , we need the theory of group [ 10,29 ] , the theory of ring [ 7,27 ] , the theory of algebra [ 30 ] and so on .

本文采用同调代数与环论相结合方法证得定理：若A是一个不可分的凝聚半局部环，且每个主理想有有限投射维数，则A是最大公因子整环。

In this paper , it is proved that if A is a indecomposable coherent semilocal ring , and every principal ideal has finite projective demension , then A is a GCD . by using homological method combined with method in ring theory .

从历史到小说的关键一环&论《资治通鉴》在三国题材演化史上的地位和作用

The Key Link from History to Novel & On the Position and Functions of Zi Zhi Tong Jian in the Theme Development of The Three Kingdoms

有限结合环类根论中的r-单环

R-simple Rings in the Radical Theory of All Associative Finite Rings

关于环的根论中的小理想

On Small Ideal in the Root Theory of Rings

本文利用半环和格论的基础知识，对半环吸收元的性质进行了探讨，得到了半环的吸收元在半环同态、强理想、正则性及格论等方面的一些较好结论。

This paper discusses the nature of semi-ring absorbable element by the application of semi-ring and lattice theory and achieves some better results in the aspects of semi-ring absorbable element in the semi-ring homology , the strong ideal , the regularity and the lattice theory .

Γ&环的一般根论

General Theory of the Radicals of Γ & rings

库仑势加新环形势的相对论束缚态

The relativistic bound states of Coulomb potential plus a new ring - shaped potential

西方文论话语“中国化”是重建中国文论话语不可或缺的一环。西方文论话语的“中国化”，不是移植西方文论话语来替换中国的文论话语；

The Chinesization of the discourse of western literary theory is an indispensable stage in the reconstruction of the discourse of Chinese literary theory .

满足多项式恒等式环的结构问题是环论一个主要内容，尤其是交换性问题。

The structural problem of PI-rings has been a main content for ring theory , in particular , for commutativity problem .

本文给出了孙子定理在数论、多项式环、一般可换环及赋值论中的若干应用。

In this article , some applications of the Chinese remainder theorem are given in the number theory , polynomial ring , commutative ring and valuation theory .

QF环已具有的美妙刻画吸引着众多环论专家展开深入的研究，并已有相关著作问世。

The well-known beautiful characterizations of QF rings have attracted many ring experts to do further researches , and some relative books have been published .

环上的广义多项式恒等式理论是环论的一个重要研究方向。

Generalized polynomial identity theory is an important branch in ring theory .

给出了实四元数环上的矩阵的Moore-Penrose逆的计算简化，某些结果对四元数环上的矩阵论的一般性研究有帮助。

A reduction for calculating the Moore-Penrose inverse of a matrix over the real quaternion field Δ is given . Some results are helpful for the general research of the matrix theory over Δ as well .