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4 Demonstratio Mathematica

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Hyper-pseudoformulas and m-solid ordered pseudovarieties

100%

Denecke K. , Phusanga D.

2011

tom Vol. 44, nr 4

723-738

In 2009 K.Denecke and J.Koppitz proved that for a monoid M of hypersubstitutions M-solid positive varieties of tree languages correspond to M-solid ordered pseudovarieties. In this paper, we will characterize M-solid ordered pseudovarieties in a similar way in which in [14] M-solid varieties, in [3] M-solid quasivarieties, in [11] M-solid pseudovarieties and in [12] M-solid algebraic systems were characterized. The main idea is to show, that we have two Galois-connections and a conjugate pair of additive closure operators. Then we can apply the general theory of conjugate pairs of additive closure operators.

Nd-hypersubstitutions of many-sorted algebras

100%

Denecke K. , Lekkoksung S.

2010

tom Vol. 43, nr 3

519-537

A non-deterministic hypersubstitution maps any operation symbol of type ? to a tree language. Non-deterministic hypersubstitutions can be extended to mappings which map tree languages to tree languages preserving the arities ([2]). We can extend those hypersubstitutions to many-sorted non-deterministic hypersubstitutions which map any operation symbol to a tree language of the corresponding sort ([5]). The aim of this paper is to show that the extension of a many-sorted non-deterministic hyper-substitution is an endomorphism of some clone and that the set of all non-deterministic hypersubstitutions of each sort forms a semigroup. These results can be applied to study M-solid many-sorted varieties of tree languages (see [4]).

Hyperidentities and hypersubstitutions in the variety of symmetric, idempotent, entropic groupoids

100%

Arworn S. , Denecke K.

1999

tom Vol. 32, nr 4

677-686

In this paper we determine the structure of the groupoid of normal form hypersubstitutions with respect to the variety of symmetric, idempotent, entropic groupoids, describe the monoid of all proper hypersubstitutions, and ask which identities are satisfied as hyperidentities.

Left-edge solid varieties of differential groupoids

100%

Arworn S. , Denecke K.

1999

tom Vol. 32, nr 1

1-11

An identity s=t is called a hyperidentity in a variety V if by substituting terms of appropriate arity for the operation symbols in s=t, one obtains an identity satisfied in V. Such substitutions are called hypersubstitutions. In the paper we consider hyperidentities and hypersubstitutions in the variety of differential groupoids, certain idempotent and medial groupoids. differential groupoids are modes as defined in [Rom-S;85]. We show that this variety and all its subvarieties are left-edge solid.