Regular completions of lattices

• Autores: John Harding, Qin Yang
• Localización: Houston journal of mathematics, ISSN 0362-1588, Vol. 38, Nº 3, 2012, págs. 685-691
• Idioma: inglés
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• Resumen

  • A variety of lattices admits a meet dense regular completion if every lattice in the variety can be embedded into a complete lattice in the variety by an embedding that is meet dense and regular (preserves existing joins and meets). We show that exactly two varieties of lattices admit a meet dense regular completion, the variety of one-element lattices and the variety of all lattices. This extends an earlier result of Harding showing these are the only two varieties of lattices closed under MacNeille completions.