本文证明了纯正么半群在其幂等元带上的局部化存在唯一，且证明了它是其最大群同态象。
This paper proves that the localization of an orthodox semigroup at the semilattice of idempotences exists and is unique which is the maximum group homomorphism image.
引进了自然序半格、偏序半群的自然序半格同态象和二次主根基等概念。
Concepts of natural ordering semilattices, natural ordering semilattice homomorphic images and principal square radicals on ordered semigroups are introduced.
刻划了具有P -正则自同态幺半群的二分图，讨论了字典序积图的自同态幺半群的P -正则性。
Bipartite graphs with P-regular endomorphism monoids are characterized. P-regularity of the endomorphism monoid of lexicographic product of graphs is discussed.
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.
利用模糊映射，给出群的模糊同态的概念，并得到模糊同态基本定理。
The concept of fuzzy homomorphism of groups is introduced based on the fuzzy mapping and the fundamental theorem of fuzzy homomorphism is given.
得到了一类自同态幺半群不是正则的图。
A family of graph which is not End-regular is constructed in this paper.
给出了有关自然偏序的的两个重要条件刻划，对具有逆断面的正则半群之间的同态进行了刻划，讨论了具有逆断面的正则半群的特殊同态像的条件。
Studying the condition about the natural partial order on it. And characterized the homomorphism between regular semigroups, discussing the conditions about the special homomorphism image.
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.
讨论模的同态的群逆存在的条件，得到正则自同态的群逆通过弱广义逆表示的显式，并给出一些应用和例子。
By using weak noncompact types conditions, we obtain an existence theorem of generalized weak solutions to (cp), improving the results of weak solutions in,.
第四节引入F -富足半群的概念，得到这类半群的若干性质，并研究f -富足半群的好同态像。
In Section 4, we introduce the concept of F-abundant semigroups. After obtaining some properties of F-abundant semigroups, the good homomorphic images of F-abundant semigroups is considered.
第四节引入F -富足半群的概念，得到这类半群的若干性质，并研究f -富足半群的好同态像。
In Section 4, we introduce the concept of F-abundant semigroups. After obtaining some properties of F-abundant semigroups, the good homomorphic images of F-abundant semigroups is considered.
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