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Notes on sectionally complemented lattices. I

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In 1944, R.P. Dilworth proved (unpublished) that every finite distributive lattice D can be represented as the congruence lattice of a finite lattice L. In 1960, G. Grätzer and E. T. Schmidt improved this result by constructing a finite  sectionally complemented lattice L whose congruence lattice represents D. In L, sectional complements do not have to be unique. The one sectional complement constructed by G. Grätzer and E. T. Schmidt in 1960, we shall call the 1960 sectional complement. This paper examines it in detail. The main result is an algebraic characterization of the 1960 sectional complement.

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Authors and Affiliations

  1. Department of Mathematics, University of Manitoba, Winnipeg MB R3T 2N2, Canada

    G. Grätzer

  2. Department of Mathematics, University of Manitoba, Winnipeg MB R3T 2N2, Canada

    H. Lakser

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  1. G. Grätzer
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  2. H. Lakser
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Grätzer, G., Lakser, H. Notes on sectionally complemented lattices. I. Acta Math Hung 108, 117–127 (2005). https://doi.org/10.1007/s10474-005-0213-z

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  • DOI: https://doi.org/10.1007/s10474-005-0213-z

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