On connections between the decomposition of an algebra into sums of direct systems of subalgebras
On countably universal Boolean algebras compact classes of models
On covariety lattices
This paper shows basic properties of covariety lattices. Such lattices are shown to be infinitely distributive. The covariety lattice of subcovarieties of a covariety K of F-coalgebras, where F:Set → Set preserves arbitrary intersections is isomorphic to the lattice of subcoalgebras of a -coalgebra for some cardinal κ. A full description of the covariety lattice of Id-coalgebras is given. For any topology τ there exist a bounded functor F:Set → Set and a covariety K of F-coalgebras, such that...
On direct limit classes of algebras
On directed convex subsets of partial monounary algebras
On distributive trices
A triple-semilattice is an algebra with three binary operations, which is a semilattice in respect of each of them. A trice is a triple-semilattice, satisfying so called roundabout absorption laws. In this paper we investigate distributive trices. We prove that the only subdirectly irreducible distributive trices are the trivial one and a two element one. We also discuss finitely generated free distributive trices and prove that a free distributive trice with two generators has 18 elements.
On embedding of lattices in simple lattices
On endomorphism structure for algebras over a fixed set
On equationally compact semigroups.
On equations of clones
On existence conditions for compatible tolerances
On exponentiation on n-ary hyperalgebras
For n-ary hyperalgebras we study a binary operation of exponentiation which to a given pair of n-ary hyperalgebras assigns their power, i.e., an n-ary hyperalgebra carried by the corresponding set of homomorphisms. We give sufficient conditions for the existence of such a power and for a decent behaviour of the exponentiation. As a consequence of our investigations we discover a cartesian closed subcategory of the category of n-ary hyperalgebras and homomorphisms between them.
On extending congruences from partial algebras
On extending endomorphisms to automorphisms.
On extending of partial Boolean algebras to partial *-algebras
On finite functions with non-trivial arity gap
Given an n-ary k-valued function f, gap(f) denotes the minimal number of essential variables in f which become fictive when identifying any two distinct essential variables in f. We particularly solve a problem concerning the explicit determination of n-ary k-valued functions f with 2 ≤ gap(f) ≤ n ≤ k. Our methods yield new combinatorial results about the number of such functions.
On finite lattices which are embeddable in subsemigroup lattices.
On frame congruences generated by frame tolerances
Nuclei of frame congruences generated by frame tolerances and by lattice congruences are constructed.
On free Turing algebras
On full partial quasigroups of finite order and local cardinal maximum codes.