Standard completions for quasiordered sets

verfasst von

Marcel Erné, Gerhard Wilke

Abstract

A standard completion for a quasiordered set Q is a closure system whose point closures are the principal ideals of Q. We characterize the following types of standard completions by means of their closure operators: (i) V-distributive completions, (ii) Completely distributive completions, (iii) A-completions (i.e. standard completions which are completely distributive algebraic lattices), (iv) Boolean completions. Moreover, completely distributive completions are described by certain idempotent relations, and the A-completions are shown to be in one-to-one correspondence with the join-dense subsets of Q. If a pseudocomplemented meet-semilattice Q has a Boolean completion C{black-letter}, then Q must be a Boolean lattice and C{black-letter} its MacNeille completion.

Organisationseinheit(en)

Institut für Algebra, Zahlentheorie und Diskrete Mathematik

Typ

Artikel

Journal

SEMIGROUP FORUM

Band

27

Seiten

351-376

Anzahl der Seiten

26

ISSN

0037-1912

Publikationsdatum

12.1983

Publikationsstatus

Veröffentlicht

Peer-reviewed

Ja

ASJC Scopus Sachgebiete

Algebra und Zahlentheorie

Elektronische Version(en)

https://doi.org/10.1007/BF02572747 (Zugang: Geschlossen)