A categorical genealogy for the congruence distributive property.
A characterization of arithmetical varieties by two-element subsets
A characterization of distributive lattices by tolerance lattices
A characterization of tolerance-distributive tree semilattices
A note on dual discriminator varieties.
A property of the solvable radical in finitely decidable varieties
It is shown that in a finitely decidable equational class, the solvable radical of any finite subdirectly irreducible member is comparable to all congruences of the irreducible if the type of the monolith is 2. In the type 1 case we establish that the centralizer of the monolith is strongly solvable.
A scheme for congruence semidistributivity
A diagrammatic statement is developed for the generalized semidistributive law in case of single algebras assuming that their congruences are permutable. Without permutable congruences, a diagrammatic statement is developed for the ∧-semidistributive law.
A ternary variety generated by lattices
Algebras presented by normal identities
Algebras satisfying certain quasiorder identities
Algebras with principal tolerances
An application of commutator theory to incidence algebras.
Usando la teoria del commutatore in algebra universale, si dimostra che una larga classe di algebre di incidenza sono polinomialmente equivalenti a moduli su anelli con divisione.
Announcements of new results
Arithmeticity at 0
Coherence in dual discriminator varieties
Coherence in varieties of algebras
Commutative directoids with sectionally antitone bijections
We study commutative directoids with a greatest element, which can be equipped with antitone bijections in every principal filter. These can be axiomatized as algebras with two binary operations satisfying four identities. A minimal subvariety of this variety is described.
Compatible Idempotent Terms in Universal Algebra
In universal algebra, we oftentimes encounter varieties that are not especially well-behaved from any point of view, but are such that all their members have a “well-behaved core”, i.e. subalgebras or quotients with satisfactory properties. Of special interest is the case in which this “core” is a retract determined by an idempotent endomorphism that is uniformly term definable (through a unary term ) in every member of the given variety. Here, we try to give a unified account of this phenomenon....
Concrete representation of some equivalence lattices
Congruence distributivity and modularity permit tolerances