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Finite Symmetric Functions with Non-Trivial Arity Gap

Shtrakov, SlavchoKoppitz, Jörg — 2012

Serdica Journal of Computing

Given an n-ary k-valued function f, gap(f) denotes the essential arity gap of f which is the minimal number of essential variables in f which become fictive when identifying any two distinct essential variables in f. In the present paper we study the properties of the symmetric function with non-trivial arity gap (2 ≤ gap(f)). We prove several results concerning decomposition of the symmetric functions with non-trivial arity gap with its minors or subfunctions. We show that all non-empty sets of...

Maximal submonoids of monoids of hypersubstitutions

Ilinka DimitrovaJörg Koppitz — 2006

Discussiones Mathematicae - General Algebra and Applications

For a monoid M of hypersubstitutions, the collection of all M-solid varieties forms a complete sublattice of the lattice L(τ) of all varieties of a given type τ. Therefore, by the study of monoids of hypersubstitutions one can get more insight into the structure of the lattice L(τ). In particular, monoids of hypersubstitutions were studied in [9] as well as in [5]. We will give a complete characterization of all maximal submonoids of the monoid Reg(n) of all regular hypersubstitutions of type τ...

On finite functions with non-trivial arity gap

Slavcho ShtrakovJörg Koppitz — 2010

Discussiones Mathematicae - General Algebra and Applications

Given an n-ary k-valued function f, gap(f) denotes the minimal number of essential variables in f which become fictive when identifying any two distinct essential variables in f. We particularly solve a problem concerning the explicit determination of n-ary k-valued functions f with 2 ≤ gap(f) ≤ n ≤ k. Our methods yield new combinatorial results about the number of such functions.

The maximal subsemigroups of the ideals of some semigroups of partial injections

Ilinka DimitrovaJörg Koppitz — 2009

Discussiones Mathematicae - General Algebra and Applications

We study the structure of the ideals of the semigroup I O n of all isotone (order-preserving) partial injections as well as of the semigroup I M n of all monotone (order-preserving or order-reversing) partial injections on an n-element set. The main result is the characterization of the maximal subsemigroups of the ideals of I O n and I M n .

Presolid varieties of n-semigroups

Avapa ChantasartrassmeeJörg Koppitz — 2005

Discussiones Mathematicae - General Algebra and Applications

he class of all M-solid varieties of a given type t forms a complete sublattice of the lattice ℒ(τ) of all varieties of algebrasof type t. This gives a tool for a better description of the lattice ℒ(τ) by characterization of complete sublattices. In particular, this was done for varieties of semigroups by L. Polák ([10]) as well as by Denecke and Koppitz ([4], [5]). Denecke and Hounnon characterized M-solid varieties of semirings ([3]) and M-solid varieties of groups were characterized by Koppitz...

Lattice-theoretically characterized classes of finite bands

Reinhard ThronJörg Koppitz — 2003

Archivum Mathematicum

There are investigated classes of finite bands such that their subsemigroup lattices satisfy certain lattice-theoretical properties which are related with the cardinalities of the Green’s classes of the considered bands, too. Mainly, there are given disjunctions of equations which define the classes of finite bands.

Pre-solid varieties of semigroups

K. DeneckeJörg Koppitz — 1995

Archivum Mathematicum

Pre-hyperidentities generalize the concept of a hyperidentity. A variety V is said to be pre-solid if every identity in V is a pre-hyperidentity. Every solid variety is pre-solid. We consider pre-solid varieties of semigroups which are not solid, determine the smallest and the largest of them, and some elements in this interval.

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Klaus DeneckeJörg KoppitzNittiya Pabhapote — 2008

Discussiones Mathematicae - General Algebra and Applications

A regular hypersubstitution is a mapping which takes every n i -ary operation symbol to an n i -ary term. A variety is called regular-solid if it contains all algebras derived by regular hypersubstitutions. We determine the greatest regular-solid variety of semigroups. This result will be used to give a new proof for the equational description of the greatest solid variety of semigroups. We show that every variety of semigroups which is finitely based by hyperidentities is also finitely based by identities....

The semantical hyperunification problem

Klaus DeneckeJörg KoppitzShelly Wismath — 2001

Discussiones Mathematicae - General Algebra and Applications

A hypersubstitution of a fixed type τ maps n-ary operation symbols of the type to n-ary terms of the type. Such a mapping induces a unique mapping defined on the set of all terms of type t. The kernel of this induced mapping is called the kernel of the hypersubstitution, and it is a fully invariant congruence relation on the (absolutely free) term algebra F τ ( X ) of the considered type ([2]). If V is a variety of type τ, we consider the composition of the natural homomorphism with the mapping induced...

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