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.
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