Tolerante Catalanzahlen
In which the binary product algebra of complex numbers, C, is generalized to a ternary product algebra, .
A number of new results that say how to transfer the entailment relation between two different finite generators of a quasi-variety of algebras is presented. As their consequence, a well-known result saying that dualisability of a quasi-variety is independent of the generating algebra is derived. The transferral of endodualisability is also considered and the results are illustrated by examples.
Results saying how to transfer the entailment in certain minimal and maximal ways and how to transfer strong dualisability between two different finite generators of a quasi-variety of algebras are presented. A new proof for a well-known result in the theory of natural dualities which says that strong dualisability of a quasi-variety is independent of the generating algebra is derived.
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....
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...