Small monoids generating varieties with uncountably many subvarieties
Sergey V. Gusev

TL;DR
This paper demonstrates that a specific small monoid, of order ten, generates a variety with uncountably many subvarieties, providing new examples and answering a recent open question in algebraic theory.
Contribution
It introduces a small, finitely based monoid of order six that generates a variety with uncountably many subvarieties, the first minimal example of its kind.
Findings
Rees quotient monoid M(aabb) of order ten is of type 2^{}
A new minimal monoid of order six with uncountably many subvarieties
First finitely based monoid of minimal size with this property
Abstract
An algebra that generates a variety with uncountably many subvarieties is said to be of type . We show that the Rees quotient monoid of order ten is of type , thereby affirmatively answering a recent question of Glasson. As a corollary, we exhibit a new example of type monoid of order six, which turns out to be minimal and the first of its kind that is finitely based.
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Taxonomy
TopicsPolynomial and algebraic computation · semigroups and automata theory
