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κ-Complete Uniquely Complemented Lattices

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Abstract

We show that for any infinite cardinal κ, every complete lattice where each element has at most one complement can be regularly embedded into a uniquely complemented κ-complete lattice. This regular embedding preserves all joins and meets, in particular it preserves the bounds of the original lattice. As a corollary, we obtain that every lattice where each element has at most one complement can be embedded into a uniquely complemented κ-complete lattice via an embedding that preserves the bounds of the original lattice.

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Authors and Affiliations

  1. Department of Mathematical Sciences, New Mexico State University, Las Cruces, NM 88003, USA

    John Harding

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  1. John Harding
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Correspondence to John Harding.

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Harding, J. κ-Complete Uniquely Complemented Lattices. Order 25, 121–129 (2008). https://doi.org/10.1007/s11083-008-9084-6

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  • DOI: https://doi.org/10.1007/s11083-008-9084-6

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