商环

Group, Subgoup, Permutation Group, Cyclic Group, Commutative Group, Normal Subgroup, Factor Group, Isomorphism, Ring, Ideal, Field, Polynomial Ring, Factor Ring.

课程内容：群，子群，置换群，循环群，交换群，正规子群，商群，群之同构，环，理想，体，多项式环，商环等。

At the same time, some properties of rough Set in quotient ring are given and proved. The fifth chapter is Rough Primary Ideals and Rough Fuzzy Primary Ideals in Semigroups, the concept of rough primary ideals and fuzzy rough primary ideals in semigroups are introduced. Under the condition of the complete congruence relation, a rough set of a primary ideal in semigroups is proved to be its primary ideal.

同时，在商环中讨论了粗糙集的一些性质，并给出这些结论的严格证明；第五章是半群中的粗准素理想和粗模糊准素理想，首次提出了半群中的粗准素理想与粗模糊准素理想的概念，证明了在完备同余关系下，半群中准素理想的粗糙集是准素理想。

Theorem 2.1.4 The following statements are equivalent for a ring R:(1) R is left co-semihereditary;(2) every finitely cogenerated factor module of a finitely cogenerated injective R-module is quasi-injective;(3) every finitely cogenerated factor module of a finitely cogenerated injective R-module is direct-injective.

an环 R下列叙述等价： l）R的每个商环是强左余半遗传的； 2）R的每个商环是左余半遗传的； 3）拟内射R模的每个有限余生成商模是拟内射的； 4）有限余生成拟内射R－模的每个有限余生成商是直内射的； 5）有限余生成fi－(来源：A3fBC论文网www.abclunwen.com)拟内射R－模的有限余生成商模是拟内射的。

Subgroup, Factor Group, Isomorphism, Ring, Ideal, Field, Polynomial Ring, Factor

课程内容：群，子群，置换群，循环群，交换群，正规子群，商群，群之同构，环，理想，体，多项式环，商环等。

In this chapter, firstly, the definition of rough rings and its properties are given. Then the definition and properties of rough subrings, rough ideals and rough quotient rings are put forward and proved. Finally, homomorphism and isomorphism of rough rings is studied.

在这一章中，首先给出了粗糙环的定义及其性质，其次给出了粗糙子环、粗糙理想、粗糙商环的定义及其性质，最后研究了粗糙环的同态与同构。

Correspondingly, the concept of fuzzy regular semiideal is introduced and the correspondence theorems of fuzzy regular semiideals and the isomorphism theorems of fuzzy regular quasi-quotient rings are established under ring homomorphism.

相应地，我们引入了模糊正则半理想概念，建立了环同态下模糊正则半理想的对应定理以及模糊正则拟商环的同构定理。

In this paper the transfer function of noulinear control system is defined over a noncommutative polynomial ring, which can be extended into its quotient ring by Ore Theorem.

本文定义了非线控制系统的传递函数，这种传递函数定义在由一个非交换多项式环扩张而成的商环上用传递函数描述了非线性控制系统的三种基本联接：串联、并联与反馈。

Analysis was done for the parameter selection of Montgomery algorithm in ringF_p /x·p(x. Through suitable algorithm parameter and representation change in ring, wereduce the complexity of multiplication in F_p /x.

分析了一类商环F_p／x·p(x上乘法的快速实现问题，通过选择合适的参数，并基于欧几里德算法改变了商环中元素的表示形式，降低了商环F_p／x·p(x上乘法运算的复杂度。

Assuming R be a semiprime ring with extended centroid C and Q be the maximal right quotient ring of R, f be a noncentral multilinear polynomial over C.d and δ are derivations of R.

给出了，假设R是带有扩张形心的半素环，Q 为R的极大右商环，f是R的扩张形心C上的非中心值的多线性多项式。

The notions of algebras of quotients and weak algebras of quotients for Lie color algebras are given.

利用经典环论中由环构造商环的方法，人们得到了李代数的商代数的概念。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。