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Algebra universalis

, 80:48 | Cite as

A completion for distributive nearlattices

  • Luciano J. GonzálezEmail author
  • Ismael Calomino
Article
  • 48 Downloads

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.

Keywords

Nearlattices Completion Extensions of operations Free lattice extension 

Mathematics Subject Classification

06A12 06B23 03G10 06A15 

Notes

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Facultad de Ciencias Exactas y NaturalesUniversidad Nacional de La PampaSanta RosaArgentina
  2. 2.CIC and Facultad de Ciencias ExactasUniversidad Nacional del CentroTandilArgentina

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