Optimal natural dualities for some quasivarities of distributive double -algebras.
Orthomodular lattices with fully nontrivial commutators
An orthomodular lattice is said to have fully nontrivial commutator if the commutator of any pair is different from zero. In this note we consider the class of all orthomodular lattices with fully nontrivial commutators. We show that this class forms a quasivariety, we describe it in terms of quasiidentities and situate important types of orthomodular lattices (free lattices, Hilbertian lattices, etc.) within this class. We also show that the quasivariety in question is not a variety answering...
Orthomodular lattices with state-separated noncompatible pairs
In the logico-algebraic foundation of quantum mechanics one often deals with the orthomodular lattices (OML) which enjoy state-separating properties of noncompatible pairs (see e.g. , and ). These properties usually guarantee reasonable “richness” of the state space—an assumption needed in developing the theory of quantum logics. In this note we consider these classes of OMLs from the universal algebra standpoint, showing, as the main result, that these classes form quasivarieties. We also illustrate...
Power pseudovarieties of semigroups I.
Power pseudovarieties of semigroups II.
Protomodular quasivarieties of universal algebras
Pseudovarieties of completely regular semigroups.
Quasiequational theories of flat algebras
We prove that finite flat digraph algebras and, more generally, finite compatible flat algebras satisfying a certain condition are finitely -based (possess a finite basis for their quasiequations). We also exhibit an example of a twelve-element compatible flat algebra that is not finitely -based.
Quasi-identities of congruence-distributive quasivarieties of algebras.
Quasivarieties of De Morgan algebras
Quasivarieties of pseudocomplemented semilattices
Two properties of the lattice of quasivarieties of pseudocomplemented semilattices are established, namely, in the quasivariety generated by the 3-element chain, there is a sublattice freely generated by ω elements and there are quasivarieties.
Quasivarieties of symmetric distributive lattices.
Relative congruence distributivity within quasivarieties of nearly associative Φ-algebras
Semidirectly closed pseudovarieties of locally trivial semigroups.
Solvability of equations in varieties of universal algebras.
Some pseudovariety joins involving the pseudovariety of finite groups.
Some quasi-ordered classes of finite commutative semigroups.
Some regular quasivarieties of commutative binary modes
Irregular (quasi)varieties of groupoids are (quasi)varieties that do not contain semilattices. The regularization of a (strongly) irregular variety of groupoids is the smallest variety containing and the variety of semilattices. Its quasiregularization is the smallest quasivariety containing and . In an earlier paper the authors described the lattice of quasivarieties of cancellative commutative binary modes, i.e. idempotent commutative and entropic (or medial) groupoids. They are all irregular...
Some results on the dot-depth hierarchy.
Subsemigroups of completely simple semigroups. III.