Partial Menger algebras of terms
| Autor: | Hippolyte Hounnon, K. Denecke |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Discrete mathematics
Generalization Computer Science::Information Retrieval General Mathematics Astrophysics::Instrumentation and Methods for Astrophysics Institut für Mathematik Computer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing) Set (abstract data type) Superposition principle TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES Linear term ComputingMethodologies_DOCUMENTANDTEXTPROCESSING Computer Science::General Literature Tuple ddc:510 ComputingMilieux_MISCELLANEOUS Mathematics |
| Popis: | The superposition operation [Formula: see text] [Formula: see text] [Formula: see text], maps to each [Formula: see text]-tuple of [Formula: see text]-ary operations on a set [Formula: see text] an [Formula: see text]-ary operation on [Formula: see text] and satisfies the so-called superassociative law, a generalization of the associative law. The corresponding algebraic structures are Menger algebras of rank [Formula: see text]. A partial algebra of type [Formula: see text] which satisfies the superassociative law as weak identity is said to be a partial Menger algebra of rank [Formula: see text]. As a generalization of linear terms we define [Formula: see text]-terms as terms where each variable occurs at most [Formula: see text]-times. It will be proved that [Formula: see text]-ary [Formula: see text]-terms form partial Menger algebras of rank [Formula: see text]. In this paper, some algebraic properties of partial Menger algebras such as generating systems, homomorphic images and freeness are investigated. As generalization of hypersubstitutions and linear hypersubstitutions we consider [Formula: see text]-hypersubstitutions. |
| Databáze: | OpenAIRE |
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