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arXiv · 2608.06982

Cross varieties of aperiodic monoids

Sergey V. Gusev
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Abstract

A variety of universal algebras is called Cross if it is finitely based, finitely generated, and has only finitely many subvarieties. A monoid is aperiodic if all its subgroups are trivial. In the present article, we show that a variety of aperiodic monoids is Cross if and only if it excludes, as subvarieties, a certain list of 22 almost Cross varieties. Consequently, this list of 22 varieties exhausts all almost Cross varieties of aperiodic monoids.

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Sergey V. Gusev. 2026-08-07. Cross varieties of aperiodic monoids. https://doi.org/10.1007/s00605-026-02220-3

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