Complete description for -equivalence types of superatomic -algebras.
Completeness theorem for the Evans logic of identities.
Constructions of (2,n)-varieties of groupoids for n = 7, 8, 9
Decidability of weak equational theories
Definability in the lattice of equational theories of semigroups.
Diassociativity is not finitely based relative to power associativity
We show that the variety of diassociative loops is not finitely based even relative to power associative loops with inverse property.
Disturbance modeling and state estimation for offset-free predictive control with state-space process models
Embedding sums of cancellative modes into semimodules
A mode (idempotent and entropic algebra) is a Lallement sum of its cancellative submodes over a normal band if it has a congruence with a normal band quotient and cancellative congruence classes. We show that such a sum embeds as a subreduct into a semimodule over a certain ring, and discuss some consequences of this fact. The result generalizes a similar earlier result of the authors proved in the case when the normal band is a semilattice.
Finitely generated congruence distributive quasivarieties of algebras
Functional representation of preiterative/combinatory formalism
Generalization of the concept of variety and quasivariety to partial algebras through category theory [Book]
Hyperidentities in associative graph algebras
Graph algebras establish a connection between directed graphs without multiple edges and special universal algebras of type (2,0). We say that a graph G satisfies an identity s ≈ t if the correspondinggraph algebra A(G) satisfies s ≈ t. A graph G is called associative if the corresponding graph algebra A(G) satisfies the equation (xy)z ≈ x(yz). An identity s ≈ t of terms s and t of any type τ is called a hyperidentity of an algebra A̲ if whenever the operation symbols occurring in s and t are replaced...
Hypersatisfaction of formulas in agebraic systems
In [2] the theory of hyperidentities and solid varieties was extended to algebraic systems and solid model classes of algebraic systems. The disadvantage of this approach is that it needs the concept of a formula system. In this paper we present a different approach which is based on the concept of a relational clone. The main result is a characterization of solid model classes of algebraic systems. The results will be applied to study the properties of the monoid of all hypersubstitutions of an...
Infinitary varieties of structures closed under the formation of complex structures
Injectivity in model theory
Lattices of relative colour-families and antivarieties
We consider general properties of lattices of relative colour-families and antivarieties. Several results generalise the corresponding assertions about colour-families of undirected loopless graphs, see [1]. Conditions are indicated under which relative colour-families form a lattice. We prove that such a lattice is distributive. In the class of lattices of antivarieties of relation structures of finite signature, we distinguish the most complicated (universal) objects. Meet decompositions in lattices...
Linear identities in graph algebras
We find the basis of all linear identities which are true in the variety of entropic graph algebras. We apply it to describe the lattice of all subvarieties of power entropic graph algebras.
Matrix identities involving multiplication and transposition
We study matrix identities involving multiplication and unary operations such as transposition or Moore–Penrose inversion. We prove that in many cases such identities admit no finite basis.
Model theoretic approach to topological functors
Modyfications of Csákány's Theorem
Varieties whose algebras have no idempotent element were characterized by B. Csákány by the property that no proper subalgebra of an algebra of such a variety is a congruence class. We simplify this result for permutable varieties and we give a local version of the theorem for varieties with nullary operations.