5 papers
Cross varieties of aperiodic monoids
Sergey V. Gusev
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…
Limit varieties of aperiodic monoids
Sergey V. Gusev, Olga B. Sapir
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 oth…
Modular elements in the lattice of monoid varieties
Sergey V. Gusev
An element of a lattice is modular if has no five-element sublattice isomorphic to the pentagon in which would correspond to the lonely midpoint. In the present wor…
Finiteness conditions for lattices of monoid varieties
Sergey V. Gusev
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 ch…
Small monoids generating varieties with uncountably many subvarieties
Sergey V. Gusev
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…