Characterization of Cross varieties of $J$-trivial monoids
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866917456012902400 |
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| author | Gusev, Sergey V. Lee, Edmond W. H. Zhang, Wen Ting |
| author_facet | Gusev, Sergey V. Lee, Edmond W. H. Zhang, Wen Ting |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_20222 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Characterization of Cross varieties of $J$-trivial monoids Gusev, Sergey V. Lee, Edmond W. H. Zhang, Wen Ting Group Theory 20M07 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. |
| title | Characterization of Cross varieties of $J$-trivial monoids |
| topic | Group Theory 20M07 |
| url | https://arxiv.org/abs/2601.20222 |