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A rotational lattice is a structure $〈 L; \lor, \land, g 〉$ where $L = 〈 L; \lor, \land 〉$ is a lattice and $g$ 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

Jaroslav Ježek, Tomáš Kepka (1989)

Czechoslovak Mathematical Journal

Varieties of idempotent medial n-quasigroups

B. Csákány, L. Megyesi (1979)

Colloquium Mathematicae

Varieties of idempotent slim groupoids

Jaroslav Ježek (2007)

Czechoslovak Mathematical Journal

Idempotent slim groupoids are groupoids satisfying $x x x ̄$ and $x (y z) x ̄ z$ . 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.

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$V$ -Lattices of varieties of algebras of different types

Varieties and finite closure conditions

Varieties generated by free completely simple semigroups.

Varieties having directly decomposable congruence classes

Varieties having distributive lattices of quasiorders

Varieties having the congruence extension property

Varieties of abelian quasigroups

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

Varieties of groupoids determined by short linear identities

Varieties of idempotent medial n-quasigroups

Varieties of idempotent slim groupoids

Varieties of $l$ -groups are torsion classes

Varieties of modular p-algebras

Varieties of Ockham algebras satisfying $x \leq f^{4} (x)$

Varieties of operator semigroups representing partitions.

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