Compact generation in partially ordered sets

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dc.identifier.uri Erné, Marcel 2018-01-29T12:30:32Z 2018-01-29T12:30:32Z 1987
dc.identifier.citation Erné, Marcel: Compact generation in partially ordered sets. In: Journal of the Australian Mathematical Society 42 (1987), Nr. 1, S. 69-83. DOI:
dc.description.abstract Several` “classical” results on algebraic complete lattices extend to algebraic posets and, more generally, to so called compactly generated posets; but, of course, there may arise difficulties in the absence of certain joins or meets. For example, the property of weak atomicity turns out to be valid in all Dedekind complete compactly generated posets, but not in arbitrary algebraic posets. The compactly generated posets are, up to isomorphism, the inductive centralized systems, where a system of sets is called centralized if it contains all point closures. A similar representation theorem holds for algebraic posets; it is known that every algebraic poset is isomorphic to the system i(Q) of all directed lower sets in some poset Q; we show that only those posets P which satisfy the ascending chain condition are isomorphic to their own “up-completion” i(P). We also touch upon a few structural aspects such as the formation of direct sums, products and substructures. The note concludes with several applications of a generalized version of the Birkhoff Frink decomposition theorem for algebraic lattices. © 1987, Australian Mathematical Society. All rights reserved. eng
dc.language.iso eng
dc.publisher Cambridge : Cambridge University Press
dc.relation.ispartofseries Journal of the Australian Mathematical Society 42 (1987), Nr. 1
dc.rights Es gilt deutsches Urheberrecht. Das Dokument darf zum eigenen Gebrauch kostenfrei genutzt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden. Dieser Beitrag ist aufgrund einer (DFG-geförderten) Allianz- bzw. Nationallizenz frei zugänglich.
dc.subject algebraic eng
dc.subject and phrases eng
dc.subject compactly generated eng
dc.subject irreducible element eng
dc.subject poset eng
dc.subject Scott completion eng
dc.subject up-complete eng
dc.subject weakly atomic eng
dc.subject.ddc 510 | Mathematik ger
dc.title Compact generation in partially ordered sets
dc.type article
dc.type Text
dc.relation.issn 1446-7887
dc.bibliographicCitation.issue 1
dc.bibliographicCitation.volume 42
dc.bibliographicCitation.firstPage 69
dc.bibliographicCitation.lastPage 83
dc.description.version publishedVersion
tib.accessRights frei zug�nglich

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