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Decompositions in Complete Lattices III. Unique Irredundant Decompositions and Convex Geometries. / Schwidefsky, M. V.
в: Algebra and Logic, Том 56, № 5, 01.11.2017, стр. 409-424.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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TY - JOUR
T1 - Decompositions in Complete Lattices III. Unique Irredundant Decompositions and Convex Geometries
AU - Schwidefsky, M. V.
PY - 2017/11/1
Y1 - 2017/11/1
N2 - 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.
AB - 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.
KW - closure space
KW - convex geometry
KW - irredundant decomposition
KW - join-semidistributive lattice
KW - locally distributive lattice
KW - lower continuous lattice
KW - minimal decomposition
KW - semimodular lattice
KW - strongly atomic lattice
KW - upper continuous lattice
KW - weakly atomic lattice
UR - http://www.scopus.com/inward/record.url?scp=85035764119&partnerID=8YFLogxK
U2 - 10.1007/s10469-017-9462-5
DO - 10.1007/s10469-017-9462-5
M3 - Article
AN - SCOPUS:85035764119
VL - 56
SP - 409
EP - 424
JO - Algebra and Logic
JF - Algebra and Logic
SN - 0002-5232
IS - 5
ER -
ID: 9672207