All varieties of orthogroups.
Amalgams of free inverse semigroups.
An algebraic version of the Cantor-Bernstein-Schröder theorem
The Cantor-Bernstein-Schröder theorem of the set theory was generalized by Sikorski and Tarski to -complete boolean algebras, and recently by several authors to other algebraic structures. In this paper we expose an abstract version which is applicable to algebras with an underlying lattice structure and such that the central elements of this lattice determine a direct decomposition of the algebra. Necessary and sufficient conditions for the validity of the Cantor-Bernstein-Schröder theorem for...
An algorithm for free algebras
We present an algorithm for constructing the free algebra over a given finite partial algebra in the variety determined by a finite list of equations. The algorithm succeeds whenever the desired free algebra is finite.
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.
An associative operator on the lattice of varieties of inverse semigroups.
An elementary proof that finite groups are projectively torsion-free
An equational basis in four variables for the three-element tournament
An example of the limit variety of semigroups.
Announcements of new results
Announcements of new results
Antiatomic retract varieties of monounary algebras
Approximate Mal'tsev operations.
Arithmeticity at 0
Automorphisms of categories of free algebras of varieties.
Balanced congruences
Let V be a variety with two distinct nullary operations 0 and 1. An algebra 𝔄 ∈ V is called balanced if for each Φ,Ψ ∈ Con(𝔄), we have [0]Φ = [0]Ψ if and only if [1]Φ = [1]Ψ. The variety V is called balanced if every 𝔄 ∈ V is balanced. In this paper, balanced varieties are characterized by a Mal'cev condition (Theorem 3). Furthermore, some special results are given for varieties of bounded lattices.
Binary hyperidentities.
Binary relations on the monoid of V-proper hypersubstitutions
In this paper we consider different relations on the set P(V) of all proper hypersubstitutions with respect to a given variety V and their properties. Using these relations we introduce the cardinalities of the corresponding quotient sets as degrees and determine the properties of solid varieties having given degrees. Finally, for all varieties of bands we determine their degrees.
Biregular and uniform identities of algebras
Birkhoff variety theorem for finite algebras