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Názov Natural extensions and profinite completions of algebras Aut.údaje B. 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 Krajina Švajčiarsko Systematika 51 Anotácia The 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 kópie 20292 Kategória ohlasu VOSMAER, 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 dát xpca - PUBLIKAČNÁ ČINNOSŤ Odkazy PERIODIKÁ-Súborný záznam periodika 
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Názov Boolean topological distributive lattices and canonical extensions Aut.údaje B. A. Davey, Miroslav Haviar, H. A. Priestley Autor Davey Brian A. (34%)
Spoluautori Haviar Miroslav 1965- (33%) UMBUV01 - Ústav vedy a výskumu
Priestley Hilary A. (33%)
Zdroj.dok. Applied Categorical Structures. Vol. 15, no. 3 (2007), pp. 225-241. - Dordrecht : Springer, 2007 Kľúč.slová topologický zväz Priestleyovská dualita kanonické rozšírenia prokonečné rozšírenie topological lattice Priestley duality canonical extension profinite completion Jazyk dok. angličtina Krajina Holandsko Systematika 515.1 Kategória publikačnej činnosti ADE Číslo archívnej kópie 6651 Kategória ohlasu JOHANSEN, Sarah M. Natural dualities for three classes of relational structures. In Algebra Universalis. ISSN 0002-5240, 2010, vol. 63, no. 2-3, pp. 149-170.
VOSMAER, 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.
RICE, Brian. Intervals of the Muchnik lattice. In Fundamenta mathematicae. ISSN 0016-2736, 2018, vol. 241, no. 2, pp. 109-126.
Katal.org. BB301 - Univerzitná knižnica Univerzity Mateja Bela v Banskej Bystrici Báza dát xpca - PUBLIKAČNÁ ČINNOSŤ Odkazy PERIODIKÁ-Súborný záznam periodika 
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