同余关系

It is proved that a semiring is complemented if and only if it is a direct product of some Boolean algebra and Boolean ring by studying the relations of congruences on the complemented semiring, so the complemented semiring is the commutative semiring.

s-内射模。通过研究可补半环S的性质及S上的同余关系，证明出可补半环与布尔环和布尔代数的直积是等价的，因而可补半环是交换半环。

An adequate version of CCS is developed, and weak bisimulation of this calculus is proved to be a congruence relation.

提出了一个CCS的变形系统，证明了系统的弱互模拟是同余关系。

An adequate version of π-calculus is developed, and bisimulation of this calculus is proved to be a congruence relation.

提出了一个π-演算的变形系统，证明了系统的互模拟是同余关系。

A ∞-semimodule over a ∞-semiring is introduced in this paper, based on which, the absorb subsemimodule and the congruence relation on a ∞-semimodule are proposed.

引入∞-半环上的∞-半模的概念，在此基础上引入吸收子半模以及∞-半模上的同余关系等概念，得到一些初步性质。

Rough ideals been first introduced by Kuroki N. Under the condition of the congruence relation, a rough set of a subsemigroup was proved to be its subsemigroup, while that of a leftideal was also proved to be its leftideal.

Kuroki N研究了半群中的粗理想，首次提出了粗子半群和粗理想的概念，证明了在同余关系下，半群的粗糙集是半群，左理想的粗糙集是左理想。

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。

Kuroki N firstly put forward the notion of rough subsets and rough ideals in semigroups, testifying that Under the condition of the congruence relation, a rough set of a subsemigroup was proved to be its subsemigroup, while that of a leftideal was also proved to be its leftideal.

Kuroki N首先研究了半群中的粗理想，首次提出了粗子半群和粗理想的概念，证明了在同余关系下，半群的粗糙集是半群，左理想的粗糙集是左理想。

In chapter two of this paper, we introduce the transitivity, which is an important definition in the 1-permutation group.

在第三章，我们介绍了格序置换群的凸同余，并研究了可迁格序置换群的凸同余与块所决定的可迁格序置换群的分类；讨论了可迁格序置换群的凸同余和块的性质以及它们之间的关系。

We investigate this kind of numbers in Chapter 4 and give the following results:(1) By generating functions theory, we have established a number of identities involving the powers of generalized Fibonacci and Lucas numbers. From these identities, we can obtain some new congruences.

第四章：利用发生函数理论以及一些运算技巧，讨论与广义Fi-bonacci，Lucas数有关的问题：(1)利用发生函数原理，建立了一系列涉及广义Fibonacci，Lucas数的幂的恒等式，并由这些恒等式得到了新的同余关系。

Two complete congruences on the congruence lattices of regular semigroups with Q-inverse transversal s are analysed.

研究了具有Q-逆断面的正则半群上的同余格Con上的等价关系W和Q，它们都是Con上的完全同余，这些完全同余的每一个类是区间，给出了每一个类的极大、极小同余的表示。

This one mode pays close attention to network credence foundation of the businessman very much.

这一模式非常关注商人的网络信用基础。

Cell morphology of bacterial ghost of Pasteurella multocida was observed by scanning electron microscopy and inactivation ratio was estimated by CFU analysi.

扫描电镜观察多杀性巴氏杆菌细菌幽灵和菌落形成单位评价遗传灭活率。