-Lattices of varieties of algebras of different types
Varieties generated by free completely simple semigroups.
Varieties of abelian quasigroups
Varieties of groupoids determined by short linear identities
Varieties of idempotent slim groupoids
Idempotent slim groupoids are groupoids satisfying and . We prove that the variety of idempotent slim groupoids has uncountably many subvarieties. We find a four-element, inherently nonfinitely based idempotent slim groupoid; the variety generated by this groupoid has only finitely many subvarieties. We investigate free objects in some varieties of idempotent slim groupoids determined by permutational equations.
Varieties of operator semigroups representing partitions.
Varieties of quasigroups determined by short strictly balanced identities