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.
Upper semicomplements and a definable element in the lattice of groupoid varieties
-Lattices of varieties of algebras of different types
Varieties generated by free completely simple semigroups.
Varieties of abelian quasigroups
Varieties of groupoids determined by short linear identities
Varieties of idempotent slim groupoids
Idempotent slim groupoids are groupoids satisfying and . We prove that the variety of idempotent slim groupoids has uncountably many subvarieties. We find a four-element, inherently nonfinitely based idempotent slim groupoid; the variety generated by this groupoid has only finitely many subvarieties. We investigate free objects in some varieties of idempotent slim groupoids determined by permutational equations.
Varieties of operator semigroups representing partitions.
Varieties of quasigroups determined by short strictly balanced identities
Weak alg-universality and -universality of semigroup quasivarieties
In an earlier paper, the authors showed that standard semigroups , and play an important role in the classification of weaker versions of alg-universality of semigroup varieties. This paper shows that quasivarieties generated by and are neither relatively alg-universal nor -universal, while there do exist finite semigroups and generating the same semigroup variety as and respectively and the quasivarieties generated by and/or are quasivar-relatively -alg-universal and -universal...