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Sheffer operation in relational structures

Identifikátory výsledku

  • Kód výsledku v IS VaVaI

    <a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F22%3A73614851" target="_blank" >RIV/61989592:15310/22:73614851 - isvavai.cz</a>

  • Výsledek na webu

    <a href="https://link.springer.com/article/10.1007/s00500-021-06466-x" target="_blank" >https://link.springer.com/article/10.1007/s00500-021-06466-x</a>

  • DOI - Digital Object Identifier

    <a href="http://dx.doi.org/10.1007/s00500-021-06466-x" target="_blank" >10.1007/s00500-021-06466-x</a>

Alternativní jazyky

  • Jazyk výsledku

    angličtina

  • Název v původním jazyce

    Sheffer operation in relational structures

  • Popis výsledku v původním jazyce

    The concept of a Sheffer operation known for Boolean algebras and orthomodular lattices is extended to arbitrary directed relational systems with involution. It is proved that to every such relational system, there can be assigned a Sheffer groupoid and also, conversely, every Sheffer groupoid induces a directed relational system with involution. Hence, investigations of these relational systems can be transformed to the treatment of special groupoids which form a variety of algebras. If the Sheffer operation is also commutative, then the induced binary relation is antisymmetric. Moreover, commutative Sheffer groupoids form a congruence distributive variety. We characterize symmetry, antisymmetry and transitivity of binary relations by identities and quasi-identities satisfied by an assigned Sheffer operation. The concepts of twist products of relational systems and of Kleene relational systems are introduced. We prove that every directed relational system can be embedded into a directed relational system with involution via the twist product construction. If the relation in question is even transitive, then the directed relational system can be embedded into a Kleene relational system. Any Sheffer operation assigned to a directed relational system A with involution induces a Sheffer operation assigned to the twist product of A.

  • Název v anglickém jazyce

    Sheffer operation in relational structures

  • Popis výsledku anglicky

    The concept of a Sheffer operation known for Boolean algebras and orthomodular lattices is extended to arbitrary directed relational systems with involution. It is proved that to every such relational system, there can be assigned a Sheffer groupoid and also, conversely, every Sheffer groupoid induces a directed relational system with involution. Hence, investigations of these relational systems can be transformed to the treatment of special groupoids which form a variety of algebras. If the Sheffer operation is also commutative, then the induced binary relation is antisymmetric. Moreover, commutative Sheffer groupoids form a congruence distributive variety. We characterize symmetry, antisymmetry and transitivity of binary relations by identities and quasi-identities satisfied by an assigned Sheffer operation. The concepts of twist products of relational systems and of Kleene relational systems are introduced. We prove that every directed relational system can be embedded into a directed relational system with involution via the twist product construction. If the relation in question is even transitive, then the directed relational system can be embedded into a Kleene relational system. Any Sheffer operation assigned to a directed relational system A with involution induces a Sheffer operation assigned to the twist product of A.

Klasifikace

  • Druh

    J<sub>imp</sub> - Článek v periodiku v databázi Web of Science

  • CEP obor

  • OECD FORD obor

    10101 - Pure mathematics

Návaznosti výsledku

  • Projekt

    <a href="/cs/project/GF20-09869L" target="_blank" >GF20-09869L: Ortomodularita z různých pohledů</a><br>

  • Návaznosti

    P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Ostatní

  • Rok uplatnění

    2022

  • Kód důvěrnosti údajů

    S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Údaje specifické pro druh výsledku

  • Název periodika

    SOFT COMPUTING

  • ISSN

    1432-7643

  • e-ISSN

    1433-7479

  • Svazek periodika

    26

  • Číslo periodika v rámci svazku

    1

  • Stát vydavatele periodika

    US - Spojené státy americké

  • Počet stran výsledku

    9

  • Strana od-do

    89-97

  • Kód UT WoS článku

    000719750300004

  • EID výsledku v databázi Scopus

    2-s2.0-85119176692