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arXiv · 2601.20222

Characterization of Cross varieties of $J$-trivial monoids

Sergey V. Gusev·Edmond W. H. Lee·Wen Ting Zhang
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Abstract

A finitely based, finitely generated variety with finitely many subvarieties is a Cross variety. In the present article, it is shown that a variety of $J$-trivial monoids is Cross if and only if it excludes as subvarieties a certain list of 14 almost Cross varieties. Consequently, the list of 14 varieties exhausts all almost Cross varieties of $J$-trivial monoids.

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Sergey V. Gusev, Edmond W. H. Lee, Wen Ting Zhang. 2026-01-28. Characterization of Cross varieties of $J$-trivial monoids. https://doi.org/10.1017/s1446788726101591

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