Asymptotische Abschätzung einer Anzahlfunktion in endlichen Relationssystemen.
Atomary tolerances on finite algebras
A tolerance on an algebra is defined similarly to a congruence, only the requirement of transitivity is omitted. The paper studies a special type of tolerance, namely atomary tolerances. They exist on every finite algebra.
Atomic compactness and elementary equivalence
Atomicity of tolerance lattices
Atomicity of tolerance lattices of commutative semigroups
Atomistic congruence lattices of semilattices.
Atomless Parts of Spaces.
Automorphism Groups of Finite Distributive Lattices with a Given Sublattice of Fixed Points.
Automorphisms of categories of free algebras of varieties.
Axiomatization of quasigroups
Quasigroups were originally described combinatorially, in terms of existence and uniqueness conditions on the solutions to certain equations. Evans introduced a universal-algebraic characterization, as algebras with three binary operations satisfying four identities. Now, quasigroups are redefined as heterogeneous algebras, satisfying just two conditions respectively known as hypercommutativity and hypercancellativity.
Axiomatizing omega and omega-op powers of words
In 1978, Courcelle asked for a complete set of axioms and rules for the equational theory of (discrete regular) words equipped with the operations of product, omega power and omega-op power. In this paper we find a simple set of equations and prove they are complete. Moreover, we show that the equational theory is decidable in polynomial time.
Axiomatizing omega and omega-op powers of words
In 1978, Courcelle asked for a complete set of axioms and rules for the equational theory of (discrete regular) words equipped with the operations of product, omega power and omega-op power. In this paper we find a simple set of equations and prove they are complete. Moreover, we show that the equational theory is decidable in polynomial time.
Baer sums and fibered aspects of Mal'cev operations
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.
Balanced d-lattices are complemented
We characterize d-lattices as those bounded lattices in which every maximal filter/ideal is prime, and we show that a d-lattice is complemented iff it is balanced iff all prime filters/ideals are maximal.
Bases in incidence structures defined on projective spaces
Betweenness spaces and tree algebras
Bijective reflexions and coreflexions of commutative unars
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.