Trees, band monoids, and formal languages.
T-Varieties and Clones of T-terms
The aim of this paper is to describe how varieties of algebras of type τ can be classified by using the form of the terms which build the (defining) identities of the variety. There are several possibilities to do so. In [3], [19], [15] normal identities were considered, i.e. identities which have the form x ≈ x or s ≈ t, where s and t contain at least one operation symbol. This was generalized in [14] to k-normal identities and in [4] to P-compatible identities. More generally, we select a subset...
Two enumeration principles for free algebras
Über die Eindeutigkeit der Lösungen algebraischer Gleichungssysteme.
Über die Existenz von freien Algebren.
Über die Lösungsmengen von Gleichungssystemen über allgemeinen Algebren.
Über die Vollständigkeit der induktiven Gruppoide der partiellen Automorphismen von Algebren
Undecidable varieties with solvable word problems. III (a semigroup variety).
Unified polynomials for congruence principality
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.
Uniqueness of improper operations
Universal and internal properties of some extensions of partially orderd sets.
Unsolid and fluid strong varieties of partial algebras.
Upper semicomplements and a definable element in the lattice of groupoid varieties
-Lattices of varieties of algebras of different types
Varieties and finite closure conditions
Varieties generated by free completely simple semigroups.
Varieties having directly decomposable congruence classes
Varieties having distributive lattices of quasiorders
Varieties having the congruence extension property