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A completion for distributive nearlattices

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Abstract

The aim of this article is to propose an adequate completion for distributive nearlattices. We give a proof of the existence of such a completion through a representation theorem, which allows us to prove that this completion is a completely distributive algebraic lattice. We show several properties about this completion, and we present a connection with the free distributive lattice extension of a distributive nearlattice. Finally, we consider how can be extended n-ary operations on distributive nearlattices, and we study the basic properties of these extensions.

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Authors and Affiliations

  1. Facultad de Ciencias Exactas y Naturales, Universidad Nacional de La Pampa, Santa Rosa, Argentina

    Luciano J. González

  2. CIC and Facultad de Ciencias Exactas, Universidad Nacional del Centro, Pinto 399, (7000), Tandil, Argentina

    Ismael Calomino

Authors
  1. Luciano J. González
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  2. Ismael Calomino
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Correspondence to Luciano J. González.

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This research was supported by the CONICET under Grant PIP 112-201501-00412. Luciano J. González was also partially supported by Universidad Nacional de La Pampa (Facultad de Ciencias Exactas y Naturales) under the Grant P.I. 64 M, Res. 432/14 CD.

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González, L.J., Calomino, I. A completion for distributive nearlattices. Algebra Univers. 80, 48 (2019). https://doi.org/10.1007/s00012-019-0622-4

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