Abstract
In [8], Vogt used so-called bialgebraic contexts to represent the lattice Sub(L) of all sublattices of a finite distributive lattice L as the substructure lattice of an appropriately defined finite (universal) algebra, based on Rival’s description (see [4] and [5]) by means of deleting suitable intervals from L. We show how to extend Vogt’s context in order to obtain a conceptually simpler description of Sub 01(L) – the lattice of all 0-1-preserving sublattices of L – by means of quasiorders and an associated total binary operation on J (L)2, the set of all pairs of non-zero join-irreducibles of L. Our approach is based on Birkhoff- resp. Priestley-duality, a standard reference is [1].
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References
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Schmid, J. (2005). Bialgebraic Contexts for Distributive Lattices – Revisited. In: Ganter, B., Godin, R. (eds) Formal Concept Analysis. ICFCA 2005. Lecture Notes in Computer Science(), vol 3403. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-32262-7_28
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DOI: https://doi.org/10.1007/978-3-540-32262-7_28
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-24525-4
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