16 citations · 102 across the 23 of their papers we have counts for
23 papers
Characterization of Cross varieties of -trivial monoids
Sergey V. Gusev, Edmond W. H. Lee, Wen Ting Zhang
A finitely based, finitely generated variety with finitely many subvarieties is a Cross variety. In the present article, it is shown that a variety of -trivial monoids is Cross…
Varieties of monoids with a distributive subvariety lattice
Sergey V. Gusev
A monoid is aperiodic if all its subgroups are trivial. We completely classify all varieties of aperiodic monoids whose subvariety lattice is distributive.
Varieties of aperiodic monoids with commuting idempotents whose subvariety lattice is distributive
Sergey V. Gusev
We completely classify all varieties of aperiodic monoids with commuting idempotents whose subvariety lattice is distributive.
Strongly nonfinitely based monoids
Sergey V. Gusev, Olga B. Sapir, Mikhail V. Volkov
We show that the 42-element monoid of all partial order preserving and extensive injections on the 4-element chain is not contained in any variety generated by a finitely based fin…
Semiring identities of semigroups of reflexive relations and upper triangular boolean matrices
S. V. Gusev
We show that the following semirings satisfy the same identities: the semiring of all reflexive binary relations on a set with elements, the semiring $\mathcal{…
The monoid of injective and extensive partial transformations of a chain with three elements is nonfinitely based
Sergey V. Gusev
We show that the monoid of all injective and extensive partial transformations of a chain with three elements admits no finite basis of its identities. This completes solving of th…
Minimal monoids generating varieties with complex subvariety lattices
Sergey V. Gusev
A variety is finitely universal if its lattice of subvarieties contains an isomorphic copy of every finite lattice. We show that the 6-element Brandt monoid generates a finitely un…
Semiring and involution identities of power groups
Sergey V. Gusev, Mikhail V. Volkov
For every group , the set of its subsets forms a semiring under set-theoretical union and element-wise multiplication and forms an involution sem…
Semiring identities of finite inverse semigroups
Sergey V. Gusev, Mikhail V. Volkov
We study the Finite Basis Problem for finite additively idempotent semirings whose multiplicative reducts are inverse semigroups. In particular, we show that each additively idempo…
Varieties of aperiodic monoids with central idempotents whose subvariety lattice is distributive
Sergey V. Gusev
We completely classify all varieties of aperiodic monoids with central idempotents whose subvariety lattice is distributive.
Distributive and lower-modular elements of the lattice of monoid varieties
Sergey V. Gusev
The sets of all neutral, distributive and lower-modular elements of the lattice of semigroup varieties are finite, countably infinite and uncountably infinite, respectively. In 201…
Limit varieties of monoids satisfying a certain identity
Sergey V. Gusev, Yu Xian Li, Wen Ting Zhang
A limit variety is a variety that is minimal with respect to being non-finitely based. Since the turn of the millennium, much attention has been given to the classification of limi…
Cancellable elements of the lattice of monoid varieties
Sergey V. Gusev, Edmond W. H. Lee
The set of all cancellable elements of the lattice of semigroup varieties has recently been shown to be countably infinite. But the description of all cancellable elements of the l…
The lattice of varieties of monoids
Sergey V. Gusev, Edmond W. H. Lee, Boris M. Vernikov
We survey results devoted to the lattice of varieties of monoids. Along with known results, some unpublished results are given with proofs. A number of open questions and problems…
Two weaker variants of congruence permutability for monoid varieties
Sergey V. Gusev, Boris M. Vernikov
We completely determine all varieties of monoids on whose free objects all fully invariant congruences or all fully invariant congruences contained in the least semilattice congrue…
Classification of limit varieties of J-trivial monoids
S. V. Gusev, O. B. Sapir
A variety of algebras is called limit if it is non-finitely based but all its proper subvarieties are finitely based. We present a new pair of limit varieties of monoids and show t…
Varieties of monoids with complex lattices of subvarieties
Sergey V. Gusev, Edmond W. H. Lee
A variety is finitely universal if its lattice of subvarieties contains an isomorphic copy of every finite lattice. Examples of finitely universal varieties of semigroups have been…
Limit varieties of aperiodic monoids with commuting idempotents
S. V. Gusev
A variety of algebras is called limit if it is non-finitely based but all its proper subvarieties are finitely based. A monoid is aperiodic if all its subgroups are trivial. We cla…
On the ascending and descending chain conditions in the lattice of monoid varieties
S. V. Gusev
In this work we consider monoids as algebras with an associative binary operation and the nullary operation that fixes the identity element. We found an example of two varieties of…
Special elements of the lattice of monoid varieties
S. V. Gusev
We completely classify all neutral or costandard elements in the lattice of all monoid varieties. Further, we prove that an arbitrary upper-modular element of $\math…
Chain varieties of monoids
Sergey V. Gusev, Boris M. Vernikov
A variety of universal algebras is called a chain variety if its subvariety lattice is a chain. Non-group chain varieties of semigroups were completely classified by Sukhanov in 19…
Cancellable elements of the lattice of semigroup varieties
Sergey V. Gusev, Dmitry V. Skokov, Boris M. Vernikov
We completely determine all commutative semigroup varieties that are cancellable elements of the lattice SEM of all semigroup varieties. In particular, we prove that, for commutati…
Endomorphisms of the lattice of epigroup varieties
S. V. Gusev, B. M. Vernikov
We examine varieties of epigroups as unary semigroups, that is semigroups equipped with an additional unary operation of pseudoinversion. The article contains two main results. The…