Finiteness conditions for lattices of monoid varieties

2025/07/24 by Sergey V. Gusev, Gusev, Sergey V.
Computer Science · Engineering · Mathematics · #08B15 #20M07 #Advanced Numerical Analysis Techniques #Algebraic Geometry and Number Theory #FOS: Mathematics #Group Theory (math.GR) #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2507.18257

openalex publication_date 2025/07/24 · openalex created_date 2025/10/16 · openalex updated_date 2026/07/28

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.

Citations

• Finitely and non-finitely related words
• Monoid varieties with extreme properties

Related

• Varieties of monoids with a distributive subvariety lattice
• Monoid varieties with extreme properties
• Varieties of aperiodic monoids with commuting idempotents whose subvariety lattice is distributive
• Limit varieties generated by finite non-J-trivial aperiodic monoids
• Limit varieties of aperiodic monoids