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Perfect extensions of de Morgan algebras

  1. TitlePerfect extensions of de Morgan algebras
    Author infoMiroslav Haviar, Miroslav Ploščica
    Author Haviar Miroslav 1965- (50%) UMBFP10 - Katedra matematiky
    Co-authors Ploščica Miroslav (50%)
    Source document Algebra Universalis. Vol. 82, no. 4 (2021), art. no. 58, pp. 1-8. - Basel : Springer Nature Switzerland AG, 2021
    Keywords De Morganova algebra - De Morgan algebra   MS-algebra   rozšírenie - extension   Boolean algebra  
    Form. Descr.články - journal articles
    LanguageEnglish
    CountrySwitzerland
    AnnotationAn algebra A is called a perfect extension of its subalgebra B if every congruence of B has a unique extension to A. This terminology was used by Blyth and Varlet [1994]. In the case of lattices, this concept was described by Grätzer and Wehrung [1999] by saying that A is a congruence-preserving extension of B. Not many investigations of this concept have been carried out so far. The present authors in another recent study faced the question of when a de Morgan algebra M is perfect extension of its Boolean subalgebra B(M), the so-called skeleton of M. In this note a full solution to this interesting problem is given. The theory of natural dualities in the sense of Davey and Werner [1983] and Clark and Davey [1998], as well as Boolean product representations, are used as the main tools to obtain the solution.
    URLLink na plný text Link na zdrojový dokument
    Public work category ADC
    No. of Archival Copy50558
    Catal.org.BB301 - Univerzitná knižnica Univerzity Mateja Bela v Banskej Bystrici
    Databasexpca - PUBLIKAČNÁ ČINNOSŤ
    ReferencesPERIODIKÁ-Súborný záznam periodika
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