完全正则半群簇格中的Self-dual簇和网
Self-dual varieties and networks in the lattice of varieties of completely regular semigroups
摘要：
各种完全正则半群格$\mathcal{L}(\mathcal{CR})$上的核关系$K$是研究$\mathcal{L}(\mathcal{CR})$结构的重要组成部分。然而，除了平凡变种的$K$类，这只是各种各样的带的晶格，内核类的详细结构一直是一个谜，直到最近。Kad'ourek [RK2]已经证明了对于$\mathcal{CR}$的两个大类的子簇，它们的核类是单例的。在其他地方（见[RK1]，[RK2]，[RK3]），我们提供了一个详细的分析的核心类的品种阿贝尔群。在这里，我们学习更一般的内核类。我们首先仔细发展的概念的对偶格的品种完全正则半群，然后表明，核类的许多品种，包括许多自对偶品种，完全正则半群包含多个副本的格品种的带作为子格。
英文摘要：
The kernel relation $K$ on the lattice $\mathcal{L}(\mathcal{CR})$ of varieties of completely regular semigroups has been a central component in many investigations into the structure of $\mathcal{L}(\mathcal{CR})$. However, apart from the $K$-class of the trivial variety, which is just the lattice of varieties of bands, the detailed structure of kernel classes has remained a mystery until recently. Kad'ourek [RK2] has shown that for two large classes of subvarieties of $\mathcal{CR}$ their kernel classes are singletons. Elsewhere (see [RK1], [RK2], [RK3]) we have provided a detailed analysis of the kernel classes of varieties of abelian groups. Here we study more general kernel classes. We begin with a careful development of the concept of duality in the lattice of varieties of completely regular semigroups and then show that the kernel classes of many varieties, including many self-dual varieties, of completely regular semigroups contain multiple copies of the lattice of varieties of bands as sublattices.
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