Linear and -linear betweenness spaces
Linear functionals in SLM-spaces
Median groups
Mixed pseudo-associativities of Bandler-Kohout compositions of relations
This paper considers compositions of relations based on the notion of the afterset and the foreset, i. e., the subproduct, the superproduct and the square product introduced by Bandler and Kohout with modification proposed by De Baets and Kerre. There are proven all possible mixed pseudo-associativity properties of Bandler – Kohout compositions of relations.
Modular median algebras
Modulare Inzidenzstrukturen
Multiple left distributive systems
We describe the free objects in the variety of algebras involving several mutually distributive binary operations. Also, we show how an associative operation can be constructed on such systems in good cases, thus obtaining a two way correspondence between LD-monoids (sets with a left self-distributive and a compatible associative operation) and multi-LD-systems (sets with a family of mutually distributive operations).
Multiplicity type and subalgebra structure in infinitary universal algebras
On a modification of axioms of general relations
Basic concepts concerning binary and ternary relations are extended to relations of arbitrary arities and then investigated.
On a modification of relational axioms
On a power of relational structures
On clones of relations
On general algebras
On interval decomposition lattices
Intervals in binary or n-ary relations or other discrete structures generalize the concept of interval in an ordered set. They are defined abstractly as closed sets of a closure system on a set V, satisfying certain axioms. Decompositions are partitions of V whose blocks are intervals, and they form an algebraic semimodular lattice. Lattice-theoretical properties of decompositions are explored, and connections with particular types of intervals are established.
On prime binary relational structures
On regularity classes of binary relations
On relations
On representation of ternary structures
On (S, A, m)-Atomic Compact Relational Systems.
On sets related to maximal clones
For an arbitrary h-ary relation ρ we are interested to express n-clone Polⁿρ in terms of some subsets of the set of all n-ary operations Oⁿ(A) on a finite set A, which are in general not clones but we can obtain Polⁿρ from these sets by using intersection and union. Therefore we specify the concept a function preserves a relation and moreover, we study the properties of this new concept and the connection between these sets and Polⁿρ. Particularly we study for arbitrary partial order relations,...