 Boolean TriplesGeorge Grätzer Chapter Chapter 6 in The Congruences of a Finite Lattice, 2016, pp 67-79 from Springer Abstract: Abstract In Part IV, we construct congruence-preserving extensions of finite lattices, extensions with special properties, such as sectionally complemented, semimodular Semimodular lattice Lattice semimodular , and so on. In Part IV, we construct congruence-preserving extensions of finite lattices, extensions with special properties, such as sectionally complemented, semimodular Semimodular lattice Lattice semimodular , and so on. It is easy to construct a proper congruence-preserving extension of a finite lattice. In the early 1990s, G. Grätzer and Schmidt, E. T. E. T. Schmidt raised the question in [126] whether every lattice has a proper congruence-preserving extension. (See also G. Grätzer and Schmidt, E. T. E. T. Schmidt [123].) It took almost a decade for the answer to appear in G. Grätzer and F. Wehrung [145]. For infinite lattices, the affirmative answer was provided by the boolean triples construction, which is described in this chapter. It is interesting that boolean triples also provide a very important tool for finite lattices. Keywords: Congruence-preserving Extension; Wehrung; Finite Lattice; Infinite Lattice; Affirmative Answer (search for similar items in EconPapers) There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it. Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-38798-7_6 Ordering information: This item can be ordered from DOI: 10.1007/978-3-319-38798-7_6 Access Statistics for this chapter More chapters in Springer Books from Springer |
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