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.
On the structure of halfdiagonal-halfterminal-symmetric categories with diagonal inversions
The category of all binary relations between arbitrary sets turns out to be a certain symmetric monoidal category Rel with an additional structure characterized by a family of diagonal morphisms, a family of terminal morphisms, and a family of diagonal inversions having certain properties. Using this properties in [11] was given a system of axioms which characterizes the abstract concept of a halfdiagonal-halfterminal-symmetric monoidal category with diagonal inversions (hdht∇s-category)....
One-generated clones of operations on binary relations
Operads and algebraic geometry.
Operations, homomorphism and update versus relational database systems
Pointwise and global sums and negatives of binary relations.
Pointwise and global sums and negatives of translation relations.
Preorders and equivalences generated by commuting relations.
Projections of relations
A projection of a relation is defined as a relation of reduced arity. The paper deals with projections of relations in coherence with their reflexivity, symmetry, completeness, regularity, cyclicity and other properties. Relationships between projections of hulls and hulls of projections are also studied.
Quasi-regular Relations – A New Class of Relations on Sets
Quotients and homomorphisms of relational systems
Relational systems containing one binary relation are investigated. Quotient relational systems are introduced and some of their properties are characterized. Moreover, homomorphisms, strong mappings and cone preserving mappings are introduced and the interplay between these notions is considered. Finally, the connection between directed relational systems and corresponding groupoids is investigated.
Random seminormed spaces
Reflexive and antisymmetric relations and their systems