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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.
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    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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