Finiteness conditions for lattices of monoid varieties
Group Theory
2025-07-25 v1
Abstract
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.
Keywords
Cite
@article{arxiv.2507.18257,
title = {Finiteness conditions for lattices of monoid varieties},
author = {Sergey V. Gusev},
journal= {arXiv preprint arXiv:2507.18257},
year = {2025}
}
Comments
16 pages. arXiv admin note: text overlap with arXiv:2308.11544, arXiv:2403.07913, arXiv:2204.11055