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Cross varieties of aperiodic monoids
Abstract
A variety of universal algebras is called Cross if it is finitely based, finitely generated, and has only finitely many subvarieties. A monoid is aperiodic if all its subgroups are trivial. In the present article, we show that a variety of aperiodic monoids is Cross if and only if it excludes, as subvarieties, a certain list of 22 almost Cross varieties. Consequently, this list of 22 varieties exhausts all almost Cross varieties of aperiodic monoids.
Versions
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BibTeX
@misc{gusev2026cross,
title = {{Cross varieties of aperiodic monoids}},
author = {Sergey V. Gusev},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.06982},
eprint = {2608.06982},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.06982},
}
RIS
TY - UNPB
TI - Cross varieties of aperiodic monoids
AU - Sergey V. Gusev
PY - 2026
DA - 2026/08/07
PB - arXiv
DO - 10.48550/arxiv.2608.06982
UR - https://arxiv.org/abs/2608.06982
AB - A variety of universal algebras is called Cross if it is finitely based, finitely generated, and has only finitely many subvarieties. A monoid is aperiodic if all its subgroups are trivial. In the present article, we show that a variety of aperiodic monoids is Cross if and only if it excludes, as subvarieties, a certain list of 22 almost Cross varieties. Consequently, this list of 22 varieties exhausts all almost Cross varieties of aperiodic monoids.
ER -