×

zbMATH — the first resource for mathematics

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
PDF BibTeX XML Cite
Full Text: EuDML
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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.