5 citations · 9 across the 8 of their papers we have counts for
8 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…
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…
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…
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…
Cross varieties of aperiodic monoids with commuting idempotents
S. V. Gusev
A variety of algebras is called Cross if it is finitely based, finitely generated, and has finitely many subvarieties. In present article, we classify all Cross varieties of aperio…
The lattice of varieties of implication semigroups
S. V. Gusev, H. P. Sankappanavar, B. M. Vernikov
In 2012, the second author introduced and examined a new type of algebras as a generalization of De Morgan algebras. These algebras are of type (2,0) with one binary and one nullar…
On the lattice of overcommutative varieties of monoids
S. V. Gusev
It is unknown so far, whether the lattice of all varieties of monoids satisfies some non-trivial identity. The objective of this note is to give the negative answer to this questio…