Decompositions in Complete Lattices II. Replaceable Irredundant Decompositions

• DOI: 10.1007/s10469-017-9443-8
• Publication Date: 2017-10-05T02:38:15Z
• Authors: M. V. Schwidefsky
• Keywords: 0102 computer and information sciences; 01 natural sciences

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.