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Pure Mathematics 2024
-正则和-反演半群
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Abstract:
格林关系在半群理论的发展中发挥着根本性作用。本文主要对几类由格林关系所确定的K-正则和K-反演半群进行了研究。首先介绍了K-正则和K-反演半群的相关概念，其次利用格林关系对K-正则半群进行了完整的刻画，同时也给出了两类特殊的K-反演半群的刻画，最后提出了刻画其他K-反演半群等相关问题。
Green’s relation plays a fundamental role in the development of semigroup theory. In this paper, several classes ofK-regular andK-inversive semigroups determined by Green’s relation are studied. Firstly, the related concepts ofK-regular andK-inversive semigroups are introduced. Secondly, a complete description ofK-regular semigroups is given by using Green’s relation. At the same time, two kinds of specialK-inversive semigroups are described. Finally, some related problems such as characterization of otherK-inversive semigroups are presented.
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