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Algebra and Discrete Mathematics, 2007, Issue 2, Pages 70–90 (Mi adm207)  
RESEARCH ARTICLE

Characterization of clones of boolean operations by identities

Runglawan Butkote, Klaus Denecke

University of Potsdam, Institute of Mathematics, 14415 Potsdam, Germany, Am Neuen Palais, 10
Full-text PDF (714 kB)
Abstract: In [4] the authors characterized all clones of Boolean operations (Boolean clones) by functional terms. In this paper we consider a Galois connection between operations and equations and characterize all Boolean clones by using of identities. For each Boolean clone we obtain a set of equations with the property that an operation $f$ belongs to this clone if and only if it satisfies these equations.
Keywords: Clone of Boolean operations, identity, Galois connection.
Bibliographic databases:
Document Type: Article
MSC: 03B05, 03C05, 08B05
Language: English
Citation: Runglawan Butkote, Klaus Denecke, “Characterization of clones of boolean operations by identities”, Algebra Discrete Math., 2007, no. 2, 70–90
Citation in format AMSBIB
\Bibitem{ButDen07}
\by Runglawan~Butkote, Klaus~Denecke
\paper Characterization of clones of boolean operations by identities
\jour Algebra Discrete Math.
\yr 2007
\issue 2
\pages 70--90
\mathnet{http://mi.mathnet.ru/adm207}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2364064}
\zmath{https://zbmath.org/?q=an:1164.08301}
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