Finiteness conditions for lattices of monoid varieties
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918103249584128 |
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| author | Gusev, Sergey V. |
| author_facet | Gusev, Sergey V. |
| contents | We classify all varieties of aperiodic monoids with central idempotents whose subvariety lattice is finite or satisfies the descending chain condition or satisfies the ascending chain condition. It turns out that for varieties in this class, the properties of having a finite subvariety lattice and a subvariety lattice satisfying the ascending chain condition are equivalent, and thus the property of having a subvariety lattice satisfying the ascending chain condition implies the one of having a subvariety lattice satisfying the descending chain condition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_18257 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Finiteness conditions for lattices of monoid varieties Gusev, Sergey V. Group Theory 20M07, 08B15 We classify all varieties of aperiodic monoids with central idempotents whose subvariety lattice is finite or satisfies the descending chain condition or satisfies the ascending chain condition. It turns out that for varieties in this class, the properties of having a finite subvariety lattice and a subvariety lattice satisfying the ascending chain condition are equivalent, and thus the property of having a subvariety lattice satisfying the ascending chain condition implies the one of having a subvariety lattice satisfying the descending chain condition. |
| title | Finiteness conditions for lattices of monoid varieties |
| topic | Group Theory 20M07, 08B15 |
| url | https://arxiv.org/abs/2507.18257 |