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Sectionally Pseudocomplemented Posets

The result's identifiers

  • Result code in IS VaVaI

    <a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F21%3A00118951" target="_blank" >RIV/00216224:14310/21:00118951 - isvavai.cz</a>

  • Alternative codes found

    RIV/61989592:15310/21:73609451

  • Result on the web

    <a href="https://link.springer.com/article/10.1007/s11083-021-09555-6" target="_blank" >https://link.springer.com/article/10.1007/s11083-021-09555-6</a>

  • DOI - Digital Object Identifier

    <a href="http://dx.doi.org/10.1007/s11083-021-09555-6" target="_blank" >10.1007/s11083-021-09555-6</a>

Alternative languages

  • Result language

    angličtina

  • Original language name

    Sectionally Pseudocomplemented Posets

  • Original language description

    The concept of a sectionally pseudocomplemented lattice was introduced in Birkhoff (1979) as an extension of relative pseudocomplementation for not necessarily distributive lattices. The typical example of such a lattice is the non-modular lattice N-5. The aim of this paper is to extend the concept of sectional pseudocomplementation from lattices to posets. At first we show that the class of sectionally pseudocomplemented lattices forms a variety of lattices which can be described by two simple identities. This variety has nice congruence properties. We summarize properties of sectionally pseudocomplemented posets and show differences to relative pseudocomplementation. We prove that every sectionally pseudocomplemented poset is completely L-semidistributive. We introduce the concept of congruence on these posets and show when the quotient structure becomes a poset again. Finally, we study the Dedekind-MacNeille completion of sectionally pseudocomplemented posets. We show that contrary to the case of relatively pseudocomplemented posets, this completion need not be sectionally pseudocomplemented but we present the construction of a so-called generalized ordinal sum which enables us to construct the Dedekind-MacNeille completion provided the completions of the summands are known.

  • 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

    Result was created during the realization of more than one project. More information in the Projects tab.

  • Continuities

    P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Others

  • Publication year

    2021

  • Confidentiality

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

Data specific for result type

  • Name of the periodical

    Order

  • ISSN

    0167-8094

  • e-ISSN

    1572-9273

  • Volume of the periodical

    38

  • Issue of the periodical within the volume

    3

  • Country of publishing house

    NL - THE KINGDOM OF THE NETHERLANDS

  • Number of pages

    20

  • Pages from-to

    527-546

  • UT code for WoS article

    000627203600002

  • EID of the result in the Scopus database

    2-s2.0-85102456470