Decompositions in Complete Lattices II. Replaceable Irredundant Decompositions

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Abstract

A characterization of lattices with replaceable irredundant decompositions is given in the following six classes: the class of upper and lower continuous lattices; the class of upper continuous completely join-semidistributive lattices; the class of upper semimodular lower continuous lattices; the class of upper semimodular completely joinsemidistributive lattices; the class of consistent lower continuous lattices; the class of consistent completely join-semidistributive lattices.

Original languageEnglish
Pages (from-to)236-244
Number of pages9
JournalAlgebra and Logic
Volume56
Issue number3
DOIs
Publication statusPublished - 1 Jul 2017

Keywords

  • consistent lattice
  • irredundant decomposition
  • join-semidistributive
  • lattice
  • lower continuous
  • semimodular
  • strongly atomic
  • upper continuous
  • weakly atomic

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