16 citations · 51 across the 17 of their papers we have counts for
17 papers · 1 filter
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 Along with known results, some unpublished results are given with proofs.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…
Cancellable elements of the lattices of varieties of semigroups and epigroups
V. Yu. Shaprynskii, D. V. Skokov, B. M. Vernikov
We completely determine all semigroup [epigroup] varieties that are cancellable elements of the lattice of all semigroup [respectively epigroup] varieties.
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…
Cancellable elements of the lattice of semigroup varieties: varieties satisfying a permutational identity of length 3
Boris M. Vernikov
We completely determine all semigroup varieties satisfiyng a permutational identity of length 3 that are cancellable elements of the lattice of all semigroup varieties. Using this…
On modular and cancellable elements of the lattice of semigroup varieties
Dmitry V. Skokov, Boris M. Vernikov
We completely determine all semigroup varieties satysfiyng a permutational identity of length 3 that are modular elements of the lattice of all semigroup varieties. Using this resu…