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.

中文翻译：

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具有复杂的子变格的Monoid变体

如果一个变体的子变体包含每个有限晶格的同构副本，则该变体是有限通用的。自1970年代初以来，就已经有了半群的有限通用变体的例子，但是尚不存在半群的有限通用变体。本文的主要目的是展示mono半球的有限普遍变体的第一个例子。这些品种的有限通用性是通过证明每个足够大的有限集上的等价关系的格点对子变量格点的某个子区间是反同构的。