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    NázovNatural extensions and profinite completions of algebras
    Aut.údajeB. A. Davey ... [et al.]
    Autor Davey Brian A. (25%)
    Spoluautori Gouveia M. J. (25%)
    Haviar Miroslav 1965- (25%) UMBFP10 - Katedra matematiky
    Priestley Hilary A. (25%)
    Zdroj.dok. Algebra Universalis. Vol. 66, no. 3 (2011), pp. 205-241. - Cham : Springer Nature Switzerland AG, 2011
    Kľúč.slová prirodzené rozšírenie   prirodzená dualita   kanonické rozšírenia   profinite completion   natural extension   natural duality   canonical extension  
    Jazyk dok.angličtina
    KrajinaŠvajčiarsko
    Systematika 51
    AnotáciaThe paper investigates profinite completions of residually finite algebras, drawing on ideas from the theory of natural dualities. Given a class A = ISP(M), where M is a set, not necessarily finite, of finite algebras, it is shown that each algebra in the class A embeds as a topologically dense subalgebra of its natural extension, and that this natural extension is isomorphic, topologically and algebraically, to the profinite completion of the original algebra. In addition it is shown how the natural extension may be concretely described as a certain family of relation-preserving maps; in the special case that M is finite and the class A possesses a single-sorted or multisorted natural duality, the relations to be preserved can be taken to be those belonging to a dualising set. For an algebra belonging to a finitely generated variety of lattice-based algebras, it is known that the profinite completion coincides with the canonical extension. In this situation the natural extension provides a new concrete realisation of the canonical extension, generalising the well-known representation of the canonical extension of a bounded distributive lattice as the lattice of up-sets of the underlying ordered set of its Priestley dual. The paper concludes with a survey of classes of algebras to which the main theorems do, and do not, apply
    Kategória publikačnej činnosti ADE
    Číslo archívnej kópie20292
    Kategória ohlasuVOSMAER, Jacob. Logic, algebra and topology : investigations into canonical extensions, duality theory and point-free topology. Amsterdam : Institute for Logic, Language and Computation, 2010. 255 s. ISBN 978-90-5776-214-7.
    Katal.org.BB301 - Univerzitná knižnica Univerzity Mateja Bela v Banskej Bystrici
    Báza dátxpca - PUBLIKAČNÁ ČINNOSŤ
    OdkazyPERIODIKÁ-Súborný záznam periodika
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