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Jakubík, Ján
Directly indecomposable direct factors of a lattice. (English). Mathematica Bohemica, vol. 121 (1996), issue 3, pp. 281-292
MSC: 06B05 | MR 1419882 | Zbl 0879.06002 | DOI: 10.21136/MB.1996.125983
Keywords:
direct product of lattices; algebraic lattice; strictly irreducible element; conditional completeness; strictly join-irreducible elements
Summary:
In this paper we generalize a result of Libkin concerning direct product decompositions of lattices.
References:
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[3] J. Jakubík: Weak product decompositions of discrete lattices. Czechoslovak Math. J. 21 (1971), 399-412. MR 0286723
[4] J. Jakubík: Weak product decompositions of partially ordered sets. Colloq. Math. 25 (1972), 177-190. DOI 10.4064/cm-25-2-177-190 | MR 0329977
[5] L. Libkin: Direct decompositions of atomistic algebraic lattices. Algebra Universalis 33 (1995), 127-135. DOI 10.1007/BF01190769 | MR 1303635 | Zbl 0818.06004
[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. DOI 10.1007/BF01848096 | MR 0652890 | Zbl 0484.06008
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