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Generalizing semidistributivity

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Abstract

A latticeL is called congruence normal if it can be generated by doubling of convex sets starting with the one-element lattice. In the special case of intervals, the lattice is called bounded. It has been proven thatL is bounded if and only ifL is congruence normal and semidistributive.

In this paper we study the connection between certain classes of convex sets and generalized semidistributive laws. These so-called doubling classes are pseudovarieties which can be described by implications as well as by forbiden substructures. In the end, we examine the structure of the lattice of all doubling classes.

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Authors and Affiliations

  1. Technische Hochschule Darmstadt, 6100, Darmstadt, Germany

    Winfried Geyer

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  1. Winfried Geyer
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Communicated by B. Jónsson

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Geyer, W. Generalizing semidistributivity. Order 10, 77–92 (1993). https://doi.org/10.1007/BF01108710

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  • DOI: https://doi.org/10.1007/BF01108710

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