The ascending varietal chain of a variety of semigroups.
The cardinalities of the Green classes of the free objects in varieties of bands.
The finite basis problem in the pseudovariety joins of aperiodic semigroups with groups.
The Galois correspondence between subvariety lattices and monoids of hpersubstitutions
Denecke and Reichel have described a method of studying the lattice of all varieties of a given type by using monoids of hypersubstitutions. In this paper we develop a Galois correspondence between monoids of hypersubstitutions of a given type and lattices of subvarieties of a given variety of that type. We then apply the results obtained to the lattice of varieties of bands (idempotent semigroups), and study the complete sublattices of this lattice obtained through the Galois correspondence.
The groupoid of 0-reduced varieties of Semigroups (n).
The join of the pseudovarieties of idempotent semigroups and locally trivial semigroups.
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 order of generalized hypersubstitutions of type .
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 word problem for regular identities
Tree transformations defined by hypersubstitutions
Tree transducers are systems which transform trees into trees just as automata transform strings into strings. They produce transformations, i.e. sets consisting of pairs of trees where the first components are trees belonging to a first language and the second components belong to a second language. In this paper we consider hypersubstitutions, i.e. mappings which map operation symbols of the first language into terms of the second one and tree transformations defined by such hypersubstitutions....
Trees, band monoids, and formal languages.