The one-block property in varieties of semigroups.
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 pseudovariety generated by completely 0-simple semigroups.
The pseudovariety is hyperdecidable
The pseudovariety of semigroups of triangular matrices over a finite field
We show that semigroups representable by triangular matrices over a fixed finite field form a decidable pseudovariety and provide a finite pseudoidentity basis for it.
The pseudovariety of semigroups of triangular matrices over a finite field
We show that semigroups representable by triangular matrices over a fixed finite field form a decidable pseudovariety and provide a finite pseudoidentity basis for it.
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 varieties of languages corresponding to the varieties of finite band monoids.
The varieties of n-testable semigroups.
The variety generated by finite nilpotent monoids.
Tolerance distributive and tolerance Boolean varieties of semigroups
Tolerance distributive and tolerance modular varieties of commutative semigroups
Tolerance modular varieties of semigroups
Trees, band monoids, and formal languages.