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Algebra Logika, 2017, Volume 56, Number 5, Pages 613–635 (Mi al819)  

Decompositions in complete lattices III. Unique irredundant decompositions and convex geometries

M. V. Schwidefskyab

a Sobolev Institute of Mathematics, pr. Akad. Koptyuga 4, Novosibirsk, 630090 Russia
b Novosibirsk State University, ul. Pirogova 1, Novosibirsk, 630090 Russia

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.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation НШ-6848.2016.1
Supported by the Grants Council (under RF President) for State Aid of Leading Scientific Schools, grant NSh-6848.2016.1.


DOI: https://doi.org/10.17377/alglog.2017.56.506

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English version:
Algebra and Logic, 2017, 56:5, 409–424

Bibliographic databases:

UDC: 512.56
Received: 05.04.2016
Revised: 10.11.2016

Citation: M. V. Schwidefsky, “Decompositions in complete lattices III. Unique irredundant decompositions and convex geometries”, Algebra Logika, 56:5 (2017), 613–635; Algebra and Logic, 56:5 (2017), 409–424

Citation in format AMSBIB
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\pages 613--635
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