Email this article Decompositions in Complete Lattices III. Unique Irredundant Decompositions and Convex Geometries
- Authors: Schwidefsky M.V.1,2
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Affiliations:
- Sobolev Institute of Mathematics
- Novosibirsk State University
- Issue: Vol 56, No 5 (2017)
- Pages: 409-424
- Section: Article
- URL: https://journal-vniispk.ru/0002-5232/article/view/234057
- DOI: https://doi.org/10.1007/s10469-017-9462-5
- ID: 234057
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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.
About the authors
M. V. Schwidefsky
Sobolev Institute of Mathematics; Novosibirsk State University
Author for correspondence.
Email: semenova@math.nsc.ru
Russian Federation, pr. Akad. Koptyuga 4, Novosibirsk, 630090; ul. Pirogova 1, Novosibirsk, 630090
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