论文标题
带有复杂次体晶格的多种形成品种
Varieties of monoids with complex lattices of subvarieties
论文作者
论文摘要
如果其子变量包含每个有限晶格的同构副本，则有限的多样性是有限的。自1970年代初以来，已经有有限通用的半群品种的例子，但是尚不清楚是否存在有限的普遍多种单型。本文的主要目的是展示有限通用的单型植物的第一个例子。这些品种的有限普遍性是通过证明每个足够大的有限套件上的等价关系的晶格对亚属体晶格的某些子室间隔的抗异态。
A variety is finitely universal if its lattice of subvarieties contains an isomorphic copy of every finite lattice. Examples of finitely universal varieties of semigroups have been available since the early 1970s, but it is unknown if there exists a finitely universal variety of monoids. The main objective of the present article is to exhibit the first examples of finitely universal varieties of monoids. The finite universality of these varieties is established by showing that the lattice of equivalence relations on every sufficiently large finite set is anti-isomorphic to some subinterval of the lattice of subvarieties.
