The reflectiveness of covering morphisms in algebra and geometry.
The semantical hyperunification problem
A hypersubstitution of a fixed type τ maps n-ary operation symbols of the type to n-ary terms of the type. Such a mapping induces a unique mapping defined on the set of all terms of type t. The kernel of this induced mapping is called the kernel of the hypersubstitution, and it is a fully invariant congruence relation on the (absolutely free) term algebra of the considered type ([2]). If V is a variety of type τ, we consider the composition of the natural homomorphism with the mapping induced...
The semigroup generated by certain operators on the congruence lattice of a Clifford semigroup.
The semigroup of varieties of weakly associative lattice groups
The set of ergodic groups of universal algebras
The set of hypergroups with operators which are constructed from a set with two elements
The Słupecki criterion by duality
A method is presented for proving primality and functional completeness theorems, which makes use of the operation-relation duality. By the result of Sierpiński, we have to investigate relations generated by the two-element subsets of only. We show how the method applies for proving Słupecki’s classical theorem by generating diagonal relations from each pair of k-tuples.
The spectrum of idempotent varieties of algebras with binary operators based on two variable identities. (Short Communication).
The spectrum of idempotent varieties of algebras with binary operators based on two variable identities.
The strong amalgamation property
The strong amalgamation property and (effective) codescent morphisms.
The structure of closure congruences
The structure of commutative ideal semigroups.
The structure of the rings assigned to group varieties
The subalgebra lattice of a finite algebra
The aim of this paper is to characterize pairs (L, A), where L is a finite lattice and A a finite algebra, such that the subalgebra lattice of A is isomorphic to L. Next, necessary and sufficient conditions are found for pairs of finite algebras (of possibly distinct types) to have isomorphic subalgebra lattices. Both of these characterizations are particularly simple in the case of distributive subalgebra lattices. We do not restrict our attention to total algebras only, but we consider the more...
The subalgebra lattice of a Heyting algebra
The submaximal clones on the three-element set with finitely many relative R-classes
For each clone C on a set A there is an associated equivalence relation analogous to Green's R-relation, which relates two operations on A if and only if each one is a substitution instance of the other using operations from C. We study the maximal and submaximal clones on a three-element set and determine which of them have only finitely many relative R-classes.
The theory of abstract algebras with infinitary operations [Book]
The theory of core algebras: its completeness.
The varieties of languages corresponding to the varieties of finite band monoids.