交换环

设R是交换环，（S，≤）是严格全序幺半群。

Let be a commutative ring and a strictly totally ordered monoid .

令k是交换环，C是k-余代数。

Abstract Let k be a commutative ring , C be a k - coalgebra .

有限交换环上的n元多项式

Polynomial Functions in n Indeterminates over Finite Commutative Rings

设R是有1的交换环，2是R的单位。

Let R be a commutative ring with 1 and let 2 be an unit of R.

总假定R为含幺有限交换环，τ为正整数。

Let R be a finite commutative ring with identity , τ be a positive integer .

交换环上Cn型李代数的标准Borel子代数的导子

Derivations of the Standard Borel Subalgebra of Lie Algebra of Type C_n over a Commutative Ring

任意交换环上的多维CRT

On the m-dimensional CRT over an arbitrary commutative ring

一个有单位元的交换环R称为α~-环，如果R是0维的并且R的每个准素理想都是素理想之幂。

A commutative ring with identity R is called an a-ring if R is zero-dimensional and each primary ideal in R is a power of a prime ideal .

交换环上Witt指数非零的二维U群的自同构

Automorphism of two-dimensional unitary groups over Commutative Rings

交换环上的Roth定理及Roth定理的扩展

Roth 's theorem on a commutative ring and its expanding

若交换环R是PMM环，则R是不可分解的且R的Picard群是幂可除的。

If R is a commutative PMM ring , then R is indecomposable and the Picard group of R is power divisible .

交换环上的Galois扩张的G－同态

The G-Homomorphisms of Galois Extensions of a Commutative Ring

一个无零因子的交换环R称为拟赋值环，如果R中有一个非零元素a，使得R的任意非零元都整除a的某个方幂。

Let R be a commutative ring without zero-divisor , R is called a quasi-valuation ring , if it contains a non-zero element a such that any non-zero element of R divides a power of a.

交换环上Chevalley代数的Borel子代数的自同构

Automorphisms of the Borel Subalgebras of Chevalley Algebras over Communicative Rings

设N（n+1）（R）是2-挠自由交换环上的n+1阶严格上三角矩阵代数。

Over a 2-torsionfree commutative ring R with identity , the algebra of all strictly upper triangular n + 1 by n + 1 matrices is denoted by N_ ( n + 1 )( R ) .

有限交换环上典型群的Sylow子群

Sylow Subgroups of Classical Groups over Finite Commutative Rings

对交换环定义了广义PF环的概念，即一切具有常数秩的有限生成投射模都为自由模的交换环。

A generalization of PF rings relative to commutative rings : rings all finitely generated projective modules with constant rank of which are free is defined .

有限交换环上CHEVALLEY群的阶

Orders of Chevalley groups over finite commutative rings

设H为有限Hopf代数，B为交换环，H0为交换、余交换的有限Hopf代数范畴，C为交换环范畴，A为交换群范畴。

Let H be a finite Hopf algebra , B a commutative ring , H 0 the category of all commutative , co-commutative finite algebra , C the category of commutative rings and A of commutative groups .

快速分组交换环网SFPring及其特性

Fast packet switch ring network SFP ring and its characteristics

基于全光缓存器的光弹性分组交换环（O-RPR）是一种全光分组交换网络，能够克服目前RPR存在的电子瓶颈。

O-RPR based on all-optical buffer is a novel all-optical packet-switching network , which is a promising network because of overcoming bottleneck of traditional RPR .

作为推论，一个形式更一般的Baer-Krull定理被推广到交换环上。

As an important consequence , a general version of Baer-Krull theorem is established in the category of commutative rings .

本文介绍了一种新型同步时隙快速分组交换环网（SFPring）及其特性。

This paper presents a new isochronous slotted fast packet switch ring network ( SFPring ) and its characteristics .

交换环上某些Chevalley代数的由正根基向量生成的幂零子代数的自同构（只有平凡的图自同构的情况）

Automorphisms of the Nilpotent Subalgebras Generated by the Positive Root Vectors of Chevalley Algebras of Some Types Over Communicative Rings ( for Case that There is Only the Trivial Graph Automorphism )

将交换环中关于一个理想的极小素理想和极大素理想的两种理论推广到DQC一环中，得到了与交换环中相近的重要结果.因而这一推广具有重要的理论意义。

This paper generalizes the theories of the minimal prime ideals of a ideal , the maximal prime ideals of a ideal in the commutative rings to DQC rings . The results in DQC rings are almost the same as those in the commutative rings .

交换环的M-赋值和高层序的相容性

Compatibility of M-valuation and higher level orders on a commutative ring

一类交换环上辛群的正规子群

The Normal Subgroup of Symplectic Groups over a Class of Commutative Rings

有零因子的交换环上w-模的链条件及其应用

Chain Conditions on w-modules of Commutative Rings with Zero Divisors and Application

交换环上的下降问题和上升问题

Problems of " pushdown " and " pullback " on a commutative ring

交换环上幂映射的周期轨道分支的对称性

The Symmetry of Components Containing Periodic Orbits of Power Maps on Com-mutative Rings