The lattice of equational theories. Part I: Modular elements
The lattice of equational theories. Part II: The lattice of full sets of terms
The lattice of equational theories. Part III: Definability and automorphisms
The lattice of equational theories. Part IV: Equational theories of finite algebras
The lattice of subvarieties of the biregularization of the variety of Boolean algebras
Let τ: F → N be a type of algebras, where F is a set of fundamental operation symbols and N is the set of all positive integers. An identity φ ≈ ψ is called biregular if it has the same variables in each of it sides and it has the same fundamental operation symbols in each of it sides. For a variety V of type τ we denote by the biregularization of V, i.e. the variety of type τ defined by all biregular identities from Id(V). Let B be the variety of Boolean algebras of type , where and . In...
The lattice of varieties and pseudovarieties of band monoids.
The lattice of varieties of fibered automata
The class of all fibered automata is a variety of two-sorted algebras. This paper provides a full description of the lattice of varieties of fibred automata.
The lattice of varieties of *-regular band monoids.
The number of minimal varieties of idempotent groupoids
The observational predicate calculus and complexity of computations (Preliminary communication)
The order of generalized hypersubstitutions of type .
The order of normalform hypersubstitutions of type (2)
In [2] it was proved that all hypersubstitutions of type τ = (2) which are not idempotent and are different from the hypersubstitution whichmaps the binary operation symbol f to the binary term f(y,x) haveinfinite order. In this paper we consider the order of hypersubstitutionswithin given varieties of semigroups. For the theory of hypersubstitution see [3].
The ordering of commutative terms
By a commutative term we mean an element of the free commutative groupoid of infinite rank. For two commutative terms , write if contains a subterm that is a substitution instance of . With respect to this relation, is a quasiordered set which becomes an ordered set after the appropriate factorization. We study definability in this ordered set. Among other things, we prove that every commutative term (or its block in the factor) is a definable element. Consequently, the ordered set has...
The order-sum in classes of partially ordered algebras.
The positive and generalized discriminators don't exist
In this paper it is proved that there does not exist a function for the language of positive and generalized conditional terms that behaves the same as the discriminator for the language of conditional terms.
The refinement of two isomorphic generalized lexicographic products
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 of varieties of weakly associative lattice groups
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.