Limit varieties of aperiodic monoids
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915902135468032 |
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| author | Gusev, Sergey V. Sapir, Olga B. |
| author_facet | Gusev, Sergey V. Sapir, Olga B. |
| contents | A limit variety is a variety that is minimal with respect to being non-finitely based. We present a new limit variety of aperiodic monoid. We also show that if there exists any other limit variety of aperiodic monoids, then it is contained in the joint of the variety $\mathbb B^1$ of all idempotent monoids and certain finitely generated variety $\mathbb E^1$ with $\mathbb B^1 \wedge \mathbb E^1 = \mathbb L_2^1$, where $\mathbb L_2^1$ is the variety of left-zero monoids. Jackson and Lee proved that $\mathbb E^1$ is HFB, that is, its every subvariety is finitely based. We exend this result a step up the classical decomposition $\mathbb B^1=\bigcup_{i \ge 2} \mathbb L^1_i$ by showing that $\mathbb E^1 \vee \overline{\mathbb E^1} \vee \mathbb L^1_3$ is also HFB, where $\overline{\mathbb E^1}$ is the variety dual of $\mathbb E^1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_06854 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Limit varieties of aperiodic monoids Gusev, Sergey V. Sapir, Olga B. Group Theory 20M07 A limit variety is a variety that is minimal with respect to being non-finitely based. We present a new limit variety of aperiodic monoid. We also show that if there exists any other limit variety of aperiodic monoids, then it is contained in the joint of the variety $\mathbb B^1$ of all idempotent monoids and certain finitely generated variety $\mathbb E^1$ with $\mathbb B^1 \wedge \mathbb E^1 = \mathbb L_2^1$, where $\mathbb L_2^1$ is the variety of left-zero monoids. Jackson and Lee proved that $\mathbb E^1$ is HFB, that is, its every subvariety is finitely based. We exend this result a step up the classical decomposition $\mathbb B^1=\bigcup_{i \ge 2} \mathbb L^1_i$ by showing that $\mathbb E^1 \vee \overline{\mathbb E^1} \vee \mathbb L^1_3$ is also HFB, where $\overline{\mathbb E^1}$ is the variety dual of $\mathbb E^1$. |
| title | Limit varieties of aperiodic monoids |
| topic | Group Theory 20M07 |
| url | https://arxiv.org/abs/2510.06854 |