On covers in the lattice of representable -varieties
On cross semigroup varieties and related questions.
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 Equational Classes of Algebraic Versions of Logic I.
On Equational Theory of Left Divisible Left Distributive Groupoids
It is an open question whether the variety generated by the left divisible left distributive groupoids coincides with the variety generated by the left distributive left quasigroups. In this paper we prove that every left divisible left distributive groupoid with the mapping surjective lies in the variety generated by the left distributive left quasigroups.
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 finitely based varieties of algebras
On frame congruences generated by frame tolerances
Nuclei of frame congruences generated by frame tolerances and by lattice congruences are constructed.