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Contexts and sublattices of concept lattices. (English) Zbl 0816.06006
Any context $$\mathcal J$$ can be uniquely assigned a complete concept lattice $$L_{\mathcal J}$$ [see, e.g., R. Wille, Ordered sets, Proc. NATO Adv. Study Inst., Banff/Can. 1981, 445-470 (1982; Zbl 0491.06008)]. In this paper we describe substructures in $$\mathcal J$$ such that their concept lattices are all complete sublattices in $$L_{\mathcal J}$$. As a consequence a characterization of contexts with distributive or modular concept lattices is obtained.
##### MSC:
 06B99 Lattices 06B05 Structure theory of lattices
##### Keywords:
context; concept lattice; substructures
Zbl 0491.06008
Full Text:
##### References:
 [1] M. Erné: Distributive Laws for Concept Lattices. Fachbereich Mathematik, Technische Hochschule Darmstadt, 1989, pp. 28. [2] F. Machala: Isomorphismen von Kontexten und Konzeptualverbänden. Acta Univ. Pal. Olomoucensis 110 (1993), 123-139. · Zbl 0798.06007 [3] R. Wille: Restructuring lattice theory: an approach based on hierarchies of concepts. I. Rival, Ordered sets, Reidel, Dordrecht-Boston, 1982, pp. 445-470. · Zbl 0491.06008
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