The degrees of regularity in varieties
The egg-box property of congruences
The equational theory of paramedial cancellation groupoids
The finite basis question for semigroups of order less than six.
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 lattice of equational theories. Part I: Modular elements
The number of minimal varieties of idempotent groupoids
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 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 word problem for regular identities
Three-variable equations of posets
We find an independent base for three-variable equations of posets.
Tolerance distributive and tolerance Boolean varieties of semigroups
Tolerance numbers, congruence -permutability and BCK-algebras
Tolerances and the Chinese remainder theorem
Transferable principal congruences and regular algebras
Transitivity of principal tolerances is not a Mal'cev property
Trapezoid lemma and congruence distributivity