On regular congruences
On regular implicit operations
On regularity classes of binary relations
On relations
On representation of ternary structures
On representations of monoids as monoids of polynomials
On reverses of some binary operators
The notion of reverse of any binary operation on the unit interval is introduced. The properties of reverses of some binary operations are studied and some applications of reverses are indicated.
On right congruences associated with the input semigroup S of automata.
On right congruences of semigroups.
On (S, A, m)-Atomic Compact Relational Systems.
On schemes for congruence distributivity
We present diagrammatic schemes characterizing congruence 3-permutable and distributive algebras. We show that a congruence 3-permutable algebra is congruence meetsemidistributive if and only if it is distributive. We characterize varieties of algebras satisfying the so-called triangular scheme by means of a Maltsev-type condition.
On semidirect and two-sided semidirect products of finite trivial monoids
On semigroups of polynomial functions.
On semigroups with minimal or maximal condition on left congruences.
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 algebras connected with the theory of harmony
On some classes of good quotient relations.
On some congruences of power algebras
In a natural way we can “lift” any operation defined on a set A to an operation on the set of all non-empty subsets of A and obtain from any algebra (A, Ω) its power algebra of subsets. In this paper we investigate extended power algebras (power algebras of non-empty subsets with one additional semilattice operation) of modes (entropic and idempotent algebras). We describe some congruence relations on these algebras such that their quotients are idempotent. Such congruences determine some class...
On some constructions of algebraic objects
Mono-unary algebras may be used to construct homomorphisms, subalgebras, and direct products of algebras of an arbitrary type.
On some correspondences between relational structures and algebras