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Sheffer operation in relational structures

The result's identifiers

  • Result code in 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>

  • Result on the web

    <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>

Alternative languages

  • Result language

    angličtina

  • Original language name

    Sheffer operation in relational structures

  • Original language description

    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.

  • Czech name

  • Czech description

Classification

  • Type

    J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database

  • CEP classification

  • OECD FORD branch

    10101 - Pure mathematics

Result continuities

  • Project

    <a href="/en/project/GF20-09869L" target="_blank" >GF20-09869L: The many facets of orthomodularity</a><br>

  • Continuities

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

Others

  • Publication year

    2022

  • Confidentiality

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

Data specific for result type

  • Name of the periodical

    SOFT COMPUTING

  • ISSN

    1432-7643

  • e-ISSN

    1433-7479

  • Volume of the periodical

    26

  • Issue of the periodical within the volume

    1

  • Country of publishing house

    US - UNITED STATES

  • Number of pages

    9

  • Pages from-to

    89-97

  • UT code for WoS article

    000719750300004

  • EID of the result in the Scopus database

    2-s2.0-85119176692