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On Finitely Generated Simple Complemented Lattices

Published online by Cambridge University Press:  20 November 2018

Werner Poguntke
Werner Poguntke*
Affiliation:
Fachbereich Mathematik der Technischen Hochschule, FB4-AG1 6100 Darmstadt, West Germany
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Let L be a lattice, and let P and Q be partially ordered sets. We say that L is generated by P if there is an isotone mapping from P into L with its image generating L. P contains Q if there is a subset Q’ of P which, with the partial ordering inherited from P, gives an isomorphic copy of Q. For an integer n > 0, the lattice of partitions of an n-element set will be denoted by II(n); it is well-known that II(rc) is simple and complemented (cf. P. Crawley-R. P. Dilworth [1; p. 96]).

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 24 , Issue 1 , 01 March 1981 , pp. 69 - 72
Copyright
Copyright © Canadian Mathematical Society 1981

References

[1] Dilworth, P. Crawley-R. P., Algebraic theory of lattices, Prentice-Hall, Englewood Cliffs, N.Y., 1973.Google Scholar
[2] Poguntke, W., On simple lattices of width three, to appear in Coll. Math. Soc. J. Bolyai, Preprint, Technische Hochschule Darmstadt (1962).Google Scholar
[3] Strietz, H., Über Erzeugendenmengen endlicher Partitionenverbände, Preprint, Technische Hochschule Darmstadt (1962).Google Scholar
[4] Wille, R., A note on simple lattices, Coll. Math. Soc. J. Bolyai, vol.14 (1962), 455-462.Google Scholar