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最后，研究了粗糙集的同态问题。Finally, the homomorphism issues on Rough sets are discussed.

本文首先定义了两个拟环之间的模糊同态映射。The concept of fuzzy homomorphism between two near-ring was defined.

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该协议建立的会话密钥是等献的、前向保密的。The homomorphism key agreement based on IBE and homomorphic encryption scheme is presented.

在第四章中，针对有向图，我们给出了满足广义同态性质的传递性签名系统。In chapter 4, we propose a transitive signature scheme that satisfies generalized homomorphism.

这些局部仿紧性在某种序同态下是保持不变的。It is abtained that these local paracompactnesses are invariable under some order homomorphism.

群G的一个元素g称为G的检验元素，如果G的每一个保持g不变的自同态都是G的自同构。An element gis a test element of a group G if every homomorphism of G which keeps g fixed is an automorphism.

同时，给出了关于RSL-代数的同态映射，刻画了同态映射的基本特性。Meanwhile, the notion of homomorphism between RSL-algebras is introduced and some of its basic properties are presented.

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群的基本同态定理是群论研究中最常见、最有价值的结论之一。The fundamental homomorphism theorem is very important consequence in group theory, by using it we can resolve many problems.

得到了同态满射下，最大理想的逆象是最大理想，并给出了最大理想的象也是最大理想的一些等价条件。This article proved that in the homomorphism of G onto H, the inverse image of a maximal ideal in H is also a maximal ideal in G.

在链表上并行操作存在非同态问题，但有些功能可以转变为几乎同态来解决。Some parallel operations are not homomorphism about lists, but some of these functions can be turned out to be almost_homomorphism.

从而对BCK-代数同志定理的推证得到了一个新的而更一般的方法。By means of which we derive and prove, with a new and general schedule of reasoning, a series of homomorphism theorems for BCK-algebras.

在＄1引入两个函数来刻划结构同态并用来讨论左C-半群的构造。In section 1, two functions are deduced to characterize the structural homomorphism and used to study the structure of left C-semigroups.

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本文得到了在同态满射下，极大正规子群的逆象也是极大正规子群，并给出了极大正规子群的象也是极大正规子群的一些等价条件。This article proves that in the homomorphism of G onto ■, the inverse image of a maximal normal subgroup in ■ is also a maximal normal subgroup in G.

本文在引入半环概念的基础上，介绍半环同态、同余关系、单同余半环等概念，讨论两个同态半环之间单同余性质的关系。This paper introduces the concept of semirings, homomorphism of semirings and congruence simple semirings, discusses the relation between two semirings.

引入了超半环，子超半环等概念，并研究了超半环的直积及超半环的同态和同构。In this paper the concepts of hyper semiring and sub-hyper semiring are introduced, and the homomorphism and isomorphism of hyper semiring are studied also.

群的基本同态定理是群论研究中最常见、最有价值的结论之一。In this paper we research mainly on the fundamental homomorphism theorem applied to direct products of groups and group of inner automorphisms of a group G.

给出了幂半群的概念，研究了幂半群的同态与同余关系，讨论了它们之间的关系，并得到了一些理想的结果。It introduces the concept of power semigroup, studies the relations between homomorphism and congruence of power semigroup and obtains some perfect results.

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地方普通话中有的词与普通话的词形同义异或义同形异，这些词是词语失误的主要对象。Those words are the main mistakes objects, which some words are homomorphism but different meanings, or different meanings but homomorphism, in local mandarin.

本文最后还证明了他们提出的两类改进型方案也不能抵御同态攻击，因而并不具有所说的安全性。Finally this paper shows that two kinds of the improved schemes proposed by Qi can not resist the homomorphism attack, and does not have the security as Qi said.

总之，在元组元素的运算上几乎同态问题比同态问题更复杂些，并且它扩充了范畴数据类型变换的应用范围。In brief, almost-homomorphism is more difficult than homomorphism on the operation of the elements of tuple, and it extends the application area of CDT translation.