2025/10/08 by Gusev, Sergey V., Sapir, Olga B.
#FOS: Mathematics #Group Theory (math.GR)
paper · doi:10.48550/arxiv.2510.06854
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 B1 of all idempotent monoids and certain finitely generated variety \mathbb E1 with \mathbb B1 \wedge \mathbb E1 = \mathbb L21, where \mathbb L21 is the variety of left-zero monoids. Jackson and Lee proved that \mathbb E1 is HFB, that is, its every subvariety is finitely based. We exend this result a step up the classical decomposition \mathbb B1=\bigcupi ≥ 2 \mathbb L1i by showing that \mathbb E1 \vee \mathbb E1 \vee \mathbb L13 is also HFB, where \mathbb E1 is the variety dual of \mathbb E1.