Commutativity of Operators on the Lattice of Existence Varieties.
Compact elements in the lattice of varieties
We prove that the lattice of varieties contains almost no compact elements.
Complexity of hypersubstitutions and lattices of varieties
Hypersubstitutions are mappings which map operation symbols to terms. The set of all hypersubstitutions of a given type forms a monoid with respect to the composition of operations. Together with a second binary operation, to be written as addition, the set of all hypersubstitutions of a given type forms a left-seminearring. Monoids and left-seminearrings of hypersubstitutions can be used to describe complete sublattices of the lattice of all varieties of algebras of a given type. The complexity...
Congruence pairs for algebras abstracting Kleene and Stone algebras
Corrigendum à l'article "Sur la construction de certaines MS-algèbres" (Port. Math., 39(1-4) (1980), 489-496)
Corrigendum to "Operators and products in the lattice of existence varieties of regular semigroups".
Corrigendum to "The join of the pseudovarieties of idempotent semigroups and locally trivial semigroups".
Covering condition in the lattice of radical classes of linearly ordered groups
Covers in the lattice of varieties of -groups.
Decidability of equational theories of coverings of semigroup varieties.
Definability for equational theories of commutative groupoids
We find several large classes of equations with the property that every automorphism of the lattice of equational theories of commutative groupoids fixes any equational theory generated by such equations, and every equational theory generated by finitely many such equations is a definable element of the lattice. We conjecture that the lattice has no non-identical automorphisms.
Definability in the lattice of equational theories of semigroups.
Distributed families of varieties of algebras
Distributive associative near lattices
Distributive differential modals
A differential modal is an algebra with two binary operations such that one of the reducts is a differential groupoid and the other is a semilattice, and with the groupoid operation distributing over the semilattice operation. The aim of this paper is to show that the varieties of entropic and distributive differential modals coincide, and to describe the lattice of varieties of entropic differential modals.
Distributive multisemilattices [Book]
Dualities in lattices of semigroup varieties.
Equational spectrum of Hilbert varieties
We prove that an equational class of Hilbert algebras cannot be defined by a single equation. In particular Hilbert algebras and implication algebras are not one-based. Also, we use a seminal theorem of Alfred Tarski in equational logic to characterize the set of cardinalities of all finite irredundant bases of the varieties of Hilbert algebras, implication algebras and commutative BCK algebras: all these varieties can be defined by independent bases of n elements, for each n > 1.
Equational Theories of Varieties defined by P-compatible Identities of Boole'an Algebras
E-varieties of regular semigroups, relatively bifree objects and fully invariant congruences.