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,...
On some correspondences between relational structures and algebras
On strong regularity of relations
There exists a natural extension of the notion of preorder from binary relations onto relations whose arities are arbitrary ordinals. In the article we find a condition under which extended preorders coincide with preorders if viewed categorically.
On symmetries and parallelogram spaces.
The notion of a TST-space is introduced and its connection with a parallelogram space is given. The existence of a TST-space is equivalent to the existence of a parallelogram space, which is a new characterization of a parallelogram space. The structure of a TST-space is described in terms of an abelian group.
On systems of mappings between models
On the characterization of primal partial algebras by strong regular hyperidentities.
On the direct power of relational systems
On the semigroup structure of cyclic left distributive algebras.
On the special context of independent sets
In this paper the context of independent sets is assigned to the complete lattice (P(M),⊆) of all subsets of a non-empty set M. Some properties of this context, especially the irreducibility and the span, are investigated.