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Orthogonality and complementation in the lattice of subspaces of a finite vector space

The result's identifiers

  • Result code in IS VaVaI

    <a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F22%3A73612701" target="_blank" >RIV/61989592:15310/22:73612701 - isvavai.cz</a>

  • Result on the web

    <a href="https://mb.math.cas.cz/full/147/2/mb147_2_1.pdf" target="_blank" >https://mb.math.cas.cz/full/147/2/mb147_2_1.pdf</a>

  • DOI - Digital Object Identifier

    <a href="http://dx.doi.org/10.21136/MB.2021.0042-20" target="_blank" >10.21136/MB.2021.0042-20</a>

Alternative languages

  • Result language

    angličtina

  • Original language name

    Orthogonality and complementation in the lattice of subspaces of a finite vector space

  • Original language description

    We investigate the lattice L(V) of subspaces of an n-dimensional vector space V over a finite field GF(q) where q is a prime power of a prime p together with the unary operation of orthogonality. It is known that this lattice is modular and that the orthogonality is an antitone involution. The lattice L(V) satisfies the chain condition and we determine the number of covers of its elements, especially the number of atoms. We characterize when orthogonality is a complementation and hence when L(V) is orthomodular. If q is a prime number and the dimension is equal to 2, we characterize orthomodularity of L(V) by a simple condition.

  • 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

    Mathematica Bohemica

  • ISSN

    0862-7959

  • e-ISSN

    2464-7136

  • Volume of the periodical

    147

  • Issue of the periodical within the volume

    2

  • Country of publishing house

    CZ - CZECH REPUBLIC

  • Number of pages

    13

  • Pages from-to

    141-153

  • UT code for WoS article

    000712891100001

  • EID of the result in the Scopus database

    2-s2.0-85130045216