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
Uniformity of congruences in coherent varieties
An algebra is uniform if for each , every two classes of have the same cardinality. It was shown by W. Taylor that coherent varieties need not be uniform (and vice versa). We show that every coherent variety having transferable congruences is uniform.
Varieties having directly decomposable congruence classes
Varieties having distributive lattices of quasiorders
Varieties having the congruence extension property
Varieties of algebras with equationally definable zeros
Varieties of groupoids determined by short linear identities
Varieties of -groups are torsion classes
Varieties of universal algebras with normal local projections.
Varieties satisfying the triangular scheme need not be congruence distributive
A diagrammatic scheme characterizing congruence distributivity of congruence permutable algebras was introduced by the first author in 2001. It is known under the name Triangular Scheme. It is known that every congruence distributive algebra satisfies this scheme and an algebra satisfying the Triangular Scheme which is not congruence distributive was found by E. K. Horváth, G. Czédli and the autor in 2003. On the other hand, it was an open problem if a variety of algebras satisfying the Triangular...