On the number of essential arguments of homomorphisms between products of median algebras
| Autor: | Gerasimos C. Meletiou, Miguel Couceiro |
|---|---|
| Přispěvatelé: | Knowledge representation, reasonning (ORPAILLEUR), Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Department of Natural Language Processing & Knowledge Discovery (LORIA - NLPKD), Laboratoire Lorrain de Recherche en Informatique et ses Applications (LORIA), Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Laboratoire Lorrain de Recherche en Informatique et ses Applications (LORIA), Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Technological Educational Institute of Epirus [Grèce], Technological Educational Institute of Epirus |
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Class (set theory)
Pure mathematics 0211 other engineering and technologies 02 engineering and technology Astrophysics::Cosmology and Extragalactic Astrophysics hypercube-freeness 01 natural sciences Boolean algebra symbols.namesake congruence distributivity 06D99 0101 mathematics Algebra over a field Algebraic number [MATH]Mathematics [math] Mathematics Algebra and Number Theory median-homomorphism 06F99 Median algebra 010102 general mathematics Subalgebra 021107 urban & regional planning essential argument Order structure symbols Homomorphism Median algebra Mathematics Subject Classification. 06A12 |
| Zdroj: | Algebra Universalis Algebra Universalis, Springer Verlag, 2018, 79 (4), pp.13. ⟨10.1007/s00012-018-0566-0⟩ Algebra Universalis, 2018, 79 (4), pp.13. ⟨10.1007/s00012-018-0566-0⟩ |
| ISSN: | 0002-5240 1420-8911 |
| Popis: | In this paper we characterize classes of median-homomorphisms between products of median algebras, that depend on a given number of arguments, by means of necessary and sufficent conditions that rely on the underlying algebraic and on the underlying order structure of median algebras. In particular, we show that a median-homomorphism that take values in a median algebra that does not contain a subalgebra isomorphic to the m-dimensional Boolean algebra as a subalgebra cannot depend on more than $$m-1$$ arguments. In view of this result, we also characterize the latter class of median algebras. We also discuss extensions of our framework on homomorphisms over median algebras to wider classes of algebras. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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