Minimal extensions of distributive bounded lattices

• Autores: M. E. Adams, J. Schmid
• Localización: Houston journal of mathematics, ISSN 0362-1588, Vol. 34, Nº 4, 2008, págs. 1009-1024
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • There is a considerable literature on (proper) maximal sublattices of distributive bounded lattices. In this note, we consider the dual concept of when L' is a minimal extension of L, that is L is a (proper) maximal sublattice of L'. Minimal extensions occur in one of two ways, so-called "removing a cover" or "splitting a point". The removal of covers is characterised and "special points" that can always be split are identified. For infinite L, there are at least |L| minimal extensions obtained by splitting special points, and examples are given to show that there need be no other minimal extensions