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

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

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 
@article{AL_2017_56_5_a5,
     author = {M. V. Schwidefsky},
     title = {Decompositions in complete {lattices~III.} {Unique} irredundant decompositions and convex geometries},
     journal = {Algebra i logika},
     pages = {613--635},
     publisher = {mathdoc},
     volume = {56},
     number = {5},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2017_56_5_a5/}
}
TY  - JOUR
AU  - M. V. Schwidefsky
TI  - Decompositions in complete lattices III. Unique irredundant decompositions and convex geometries
JO  - Algebra i logika
PY  - 2017
SP  - 613
EP  - 635
VL  - 56
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AL_2017_56_5_a5/
LA  - ru
ID  - AL_2017_56_5_a5
ER  - 
%0 Journal Article
%A M. V. Schwidefsky
%T Decompositions in complete lattices III. Unique irredundant decompositions and convex geometries
%J Algebra i logika
%D 2017
%P 613-635
%V 56
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AL_2017_56_5_a5/
%G ru
%F AL_2017_56_5_a5
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/