16 citations · 102 across the 23 of their papers we have counts for
6 papers · 2 filters
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…