论文标题
完全常规半群的晶格中的自偶式品种和网络
Self-dual varieties and networks in the lattice of varieties of completely regular semigroups
论文作者
论文摘要
晶格$ \ Mathcal {l}（\ Mathcal {cr}）的内核关系$ k $在许多调查中对$ \ MATHCAL {l}结构的许多调查中的核心组件（\ Mathcal {cr {Cr}）$。但是，除了琐碎的品种的$ k $类别（这只是乐队品种的格子）外，直到最近，内核课程的详细结构仍然是一个谜。 Kad'ourek [rk2]表明，对于两个$ \ Mathcal {Cr} $的两个大型次视角，它们的内核类都是单例。在其他地方（请参阅[RK1]，[RK2]，[RK3]），我们对Abelian群体种类的核类别提供了详细的分析。在这里，我们研究了更多一般的内核课程。我们首先要仔细地发展了完全规则的半群的各种二元性概念，然后表明，完全规则的半群中的许多品种的内核类别（包括许多自偶会品种）包含多种频段品种的晶状体副本。
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.
