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

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{AL_2017_56_3_a4,
     author = {M. V. Schwidefsky},
     title = {Decompositions in complete {lattices.~II.} {Replaceable} irredundant decompositions},
     journal = {Algebra i logika},
     pages = {354--366},
     publisher = {mathdoc},
     volume = {56},
     number = {3},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2017_56_3_a4/}
}
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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/