反半群的正扩展和全限制半间接积

Mária B. Szendrei
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引用次数: 0

摘要

我们描述了与完全受限半间接积同构的逆半群的正扩展,并提出了一个卡卢兹宁-克拉斯诺定理,它比比尔哈特提出的著名嵌入定理适用于更多的逆半群的正扩展,而且还在两个方面加强了该结果。首先,我们的结果中应用的花环积构造源于霍顿的花环积,是一个完全的有限半间接积,而不仅仅是一个λ半间接积。其次,我们的花环积构造中的核类是要嵌入的正扩展的某些核类的直接积,而不仅仅是其整个核的直接幂的逆子半群。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Normal extensions and full restricted semidirect products of inverse semigroups
We characterize the normal extensions of inverse semigroups isomorphic to full restricted semidirect products, and present a Kalouznin-Krasner theorem which holds for a wider class of normal extensions of inverse semigroups than that in the well-known embedding theorem due to Billhardt, and also strengthens that result in two respects. First, the wreath product construction applied in our result, and stemmming from Houghton's wreath product, is a full restricted semidirect product not merely a lambda-semidirect product. Second, the Kernel classes of our wreath product construction are direct products of some Kernel classes of the normal extension to be embedded rather than only inverse subsemigroups of the direct power of its whole Kernel.
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