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Title: Directly indecomposable direct factors of a lattice (English)
Author: Jakubík, Ján
Language: English
Journal: Mathematica Bohemica
ISSN: 0862-7959 (print)
ISSN: 2464-7136 (online)
Volume: 121
Issue: 3
Year: 1996
Pages: 281-292
Summary lang: English
Category: math
Summary: In this paper we generalize a result of Libkin concerning direct product decompositions of lattices. (English)
Keyword: direct product of lattices
Keyword: algebraic lattice
Keyword: strictly irreducible element
Keyword: conditional completeness
Keyword: strictly join-irreducible elements
MSC: 06B05
idZBL: Zbl 0879.06002
idMR: MR1419882
DOI: 10.21136/MB.1996.125983
Date available: 2009-09-24T21:19:44Z
Last updated: 2020-07-29
Stable URL:
Reference: [1] G. Grätzer: General Lattice Theory.Birkhäuser Verlag, Basel, 1978. MR 0504338
Reference: [2] J. Hashimoto: On direct product decompositions of partially ordered sets.Ann. of Math. 54 (1951), 315-318. MR 0043067, 10.2307/1969532
Reference: [3] J. Jakubík: Weak product decompositions of discrete lattices.Czechoslovak Math. J. 21 (1971), 399-412. MR 0286723
Reference: [4] J. Jakubík: Weak product decompositions of partially ordered sets.Colloq. Math. 25 (1972), 177-190. MR 0329977, 10.4064/cm-25-2-177-190
Reference: [5] L. Libkin: Direct decompositions of atomistic algebraic lattices.Algebra Universalis 33 (1995), 127-135. Zbl 0818.06004, MR 1303635, 10.1007/BF01190769
Reference: [6] G. Richter: On the structure of lattices in which every element is a join of join-irreducible elements.Period. Math. Hungar. 13 (1982), 47-69. Zbl 0484.06008, MR 0652890, 10.1007/BF01848096


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