Standard

Decompositions in Complete Lattices III. Unique Irredundant Decompositions and Convex Geometries. / Schwidefsky, M. V.

In: Algebra and Logic, Vol. 56, No. 5, 01.11.2017, p. 409-424.

Research output: Contribution to journal › Article › peer-review

Harvard

Schwidefsky, MV 2017, 'Decompositions in Complete Lattices III. Unique Irredundant Decompositions and Convex Geometries', Algebra and Logic, vol. 56, no. 5, pp. 409-424. https://doi.org/10.1007/s10469-017-9462-5

APA

Schwidefsky, M. V. (2017). Decompositions in Complete Lattices III. Unique Irredundant Decompositions and Convex Geometries. Algebra and Logic, 56(5), 409-424. https://doi.org/10.1007/s10469-017-9462-5

Vancouver

Schwidefsky MV. Decompositions in Complete Lattices III. Unique Irredundant Decompositions and Convex Geometries. Algebra and Logic. 2017 Nov 1;56(5):409-424. doi: 10.1007/s10469-017-9462-5

Author

Schwidefsky, M. V. / Decompositions in Complete Lattices III. Unique Irredundant Decompositions and Convex Geometries. In: Algebra and Logic. 2017 ; Vol. 56, No. 5. pp. 409-424.

BibTeX

@article{95c00e99253040b1a40e1516bea428f7,
title = "Decompositions in Complete Lattices III. Unique Irredundant Decompositions and Convex Geometries",
abstract = "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, minimal decomposition, semimodular lattice, strongly atomic lattice, upper continuous lattice, weakly atomic lattice",
author = "Schwidefsky, {M. V.}",
year = "2017",
month = nov,
day = "1",
doi = "10.1007/s10469-017-9462-5",
language = "English",
volume = "56",
pages = "409--424",
journal = "Algebra and Logic",
issn = "0002-5232",
publisher = "Springer US",
number = "5",

}

RIS

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