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Tensorial decomposition of concept lattices

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Abstract

A tensor product for complete lattices is studied via concept lattices. A characterization as a universal solution and an ideal representation of the tensor products are given. In a large class of concept lattices which contains all finite ones, the subdirect decompositions of a tensor product can be determined by the subdirect decompositions of its factors. As a consequence, one obtains that the tensor product of completely subdirectly irreducible concept lattices of this class is again completely subdirectly irreducible. Finally, applications to conceptual measurement are discussed.

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Authors and Affiliations

  1. Fachbereich Mathematik, Technische Hochschule Darmstadt, Schlossgartenstr. 7, D-6100, Darmstadt, West Germany

    Rudolf Wille

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  1. Rudolf Wille
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Communicated by R. P. Dilworth

Dedicated to Ernst-August Behrens on the occasion of his seventieth birthday.

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Wille, R. Tensorial decomposition of concept lattices. Order 2, 81–95 (1985). https://doi.org/10.1007/BF00337926

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  • DOI: https://doi.org/10.1007/BF00337926

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