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.
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Translated from Algebra i Logika, Vol. 56, No. 3, pp. 354-366, May-June, 2017.
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Schwidefsky, M.V. Decompositions in Complete Lattices II. Replaceable Irredundant Decompositions. Algebra Logic 56, 236–244 (2017). https://doi.org/10.1007/s10469-017-9443-8
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DOI: https://doi.org/10.1007/s10469-017-9443-8