Varieties of algebras with equationally definable zeros
Varieties of an enriched category
Varieties of associative rings closed under ideal sums
Varieties of completely regular semigroups generated by Mal'cev products.
Varieties of distributive lattices with unary operations. II.
Varieties of Distributive Rotational Lattices
A rotational lattice is a structure where is a lattice and is a lattice automorphism of finite order. We describe the subdirectly irreducible distributive rotational lattices. Using Jónsson’s lemma, this leads to a description of all varieties of distributive rotational lattices.
Varieties of groupoids determined by short linear identities
Varieties of idempotent medial n-quasigroups
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 -groups are torsion classes
Varieties of modular p-algebras
Varieties of Ockham algebras satisfying
Varieties of operator semigroups representing partitions.
Varieties of quasigroups determined by short strictly balanced identities
Varieties of universal algebras with normal local projections.
Varieties satisfying ideal equalities
Varieties satisfying the triangular scheme need not be congruence distributive
A diagrammatic scheme characterizing congruence distributivity of congruence permutable algebras was introduced by the first author in 2001. It is known under the name Triangular Scheme. It is known that every congruence distributive algebra satisfies this scheme and an algebra satisfying the Triangular Scheme which is not congruence distributive was found by E. K. Horváth, G. Czédli and the autor in 2003. On the other hand, it was an open problem if a variety of algebras satisfying the Triangular...
Varieties which are locally regular and permutable at 0
Varieties with modular and distributive lattices of symmetric or reflexive relations
Varieties with polynomially many models, I
A characterization of locally finite congruence modular varieties with the number of at most k-generated models being bounded from above by a polynomial in k is given. These are exactly the varieties polynomially equivalent to the varieties of unitary modules over a finite ring of finite representation type.