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Decompositions in Complete Lattices III. Unique Irredundant Decompositions and Convex Geometries

Authors
  • Schwidefsky, M. V.1, 2
  • 1 Sobolev Institute of Mathematics, pr. Akad. Koptyuga 4, Novosibirsk, 630090, Russia , Novosibirsk (Russia)
  • 2 Novosibirsk State University, ul. Pirogova 1, Novosibirsk, 630090, Russia , Novosibirsk (Russia)
Type
Published Article
Journal
Algebra and Logic
Publisher
Springer US
Publication Date
Nov 01, 2017
Volume
56
Issue
5
Pages
409–424
Identifiers
DOI: 10.1007/s10469-017-9462-5
Source
Springer Nature
Keywords
License
Yellow

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.

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