Algebraic duality of constant algebras
Algebras presented by normal identities
Algebras satisfying certain quasiorder identities
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 equational basis in four variables for the three-element tournament
Announcements of new results
Approximate Mal'tsev operations.
Arithmeticity at 0
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.
Biregular and uniform identities of algebras
Birkhoff variety theorem for finite algebras
Central extensions in Mal'tsev varieties.
Centrality and normality in protomodular categories.
Characterization of pointed varieties of universal algebras with normal projections.
Characterization of protomodular varieties of universal algebras.
Characterizing tolerance trivial finite algebras
An algebra is tolerance trivial if where is the lattice of all tolerances on . If contains a Mal’cev function compatible with each , then is tolerance trivial. We investigate finite algebras satisfying also the converse statement.
Classes of graphs definable by graph algebra identities or quasi-identities
Closedness properties of internal relations. I. A unified approach to Mal'tsev, unital and subtractive categories.
Closedness properties of internal relations. II: Bourn localization.