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Algebra i logika, 2017, Volume 56, Number 3, Pages 354–366
DOI: https://doi.org/10.17377/alglog.2017.56.305 (Mi al796) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Decompositions in complete lattices. II. Replaceable irredundant decompositions

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
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DOI: https://doi.org/10.17377/alglog.2017.56.305
Abstract: A characterization of lattices with replaceable irredundant decompositions is given in the following six classes:
– the class of upper and lower continuous lattices;
– the class of upper continuous join-semidistributive lattices;
– the class of upper semimodular lower continuous lattices;
– the class of upper semimodular join-semidistributive lattices;
– the class of consistent lower continuous lattices;
– the class of consistent join-semidistributive lattices.
Keywords: consistent lattice, irredundant decomposition, join-semidistributive, lattice, lower continuous, semimodular, strongly atomic, upper continuous, weakly atomic.
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.
Received: 05.04.2016
Revised: 10.11.2016
English version:
Algebra and Logic, 2017, Volume 56, Issue 3, Pages 236–244
DOI: https://doi.org/10.1007/s10469-017-9443-8
Bibliographic databases:
Document Type: Article
UDC: 512.56
Language: Russian
Citation: M. V. Schwidefsky, “Decompositions in complete lattices. II. Replaceable irredundant decompositions”, Algebra Logika, 56:3 (2017), 354–366; Algebra and Logic, 56:3 (2017), 236–244
Citation in format AMSBIB
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    		Алгебра и логика Algebra and Logic
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