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Finite distributive lattices are congruence lattices of almost-geometric lattices

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Abstract

A semimodular lattice L of finite length will be called an almost-geometric lattice if the order J(L) of its nonzero join-irreducible elements is a cardinal sum of at most two-element chains. We prove that each finite distributive lattice is isomorphic to the lattice of congruences of a finite almost-geometric lattice.

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Authors and Affiliations

  1. Bolyai Institute, University of Szeged, Aradi vértanúk tere 1, Szeged, 6720, Hungary

    Gábor Czédli

  2. Mathematical Institute of the Budapest University of Technology and Economics, Műegyetem rkp. 3, H-1521, Budapest, Hungary

    E. Tamás Schmidt

Authors
  1. Gábor Czédli
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  2. E. Tamás Schmidt
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Correspondence to Gábor Czédli.

Additional information

Communicated by M. Ploscica.

This research was partially supported by the NFSR of Hungary (OTKA), grant nos. T 049433 and K 60148.

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Czédli, G., Tamás Schmidt, E. Finite distributive lattices are congruence lattices of almost-geometric lattices. Algebra Univers. 65, 91–108 (2011). https://doi.org/10.1007/s00012-011-0119-2

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  • DOI: https://doi.org/10.1007/s00012-011-0119-2

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