Geodesic
Decompositions in complete lattices~III. Unique irredundant decompositions and convex geometries
Algebra i logika, Tome 56 (2017) no. 5, pp. 613-635.

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We give a characterization of complete strongly dually atomic lattices having unique irredundant decompositions which are also canonical. It is shown that all known characterizations of lattices with unique irredundant decompositions are a consequence of this result. In addition, upper continuous closure lattices of convex geometries with (unique) irredundant decompositions are characterized.
Keywords: closure space, convex geometry, irredundant decomposition, join-semidistributive lattice, locally distributive lattice, lower continuous lattice, semimodular lattice, strongly atomic lattice, upper continuous lattice, weakly atomic lattice.
Mots-clés : minimal decomposition 
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M. V. Schwidefsky. Decompositions in complete lattices~III. Unique irredundant decompositions and convex geometries. Algebra i logika, Tome 56 (2017) no. 5, pp. 613-635. http://geodesic.mathdoc.fr/item/AL_2017_56_5_a5/

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