Geodesic
Decompositions in complete lattices.~II. Replaceable irredundant decompositions
Algebra i logika, Tome 56 (2017) no. 3, pp. 354-366.

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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 join-semidistributive lattices; – the class of upper semimodular lower continuous lattices; – the class of upper semimodular join-semidistributive lattices; – the class of consistent lower continuous lattices; – the class of consistent join-semidistributive lattices.
Keywords: consistent lattice, irredundant decomposition, join-semidistributive, lattice, lower continuous, semimodular, strongly atomic, upper continuous, weakly atomic. 
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M. V. Schwidefsky. Decompositions in complete lattices.~II. Replaceable irredundant decompositions. Algebra i logika, Tome 56 (2017) no. 3, pp. 354-366. http://geodesic.mathdoc.fr/item/AL_2017_56_3_a4/

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