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Finite sublattices of three-generated lattices

Published online by Cambridge University Press:  09 April 2009

Brian A. Davey  and
Ivan Rival
Brian A. Davey
Affiliation:
Department of MathematicsUniversity of Manitoba Winnipeg, Manitoba, R3T 2N2, Canada.
Ivan Rival
Affiliation:
Department of MathematicsUniversity of Manitoba Winnipeg, Manitoba, R3T 2N2, Canada.
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Abstract

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Every lattice generated by three unordered elements contains a finite sublattice generated by three unordered elements. A list ℒ of twelve finite lattices, each generated by a three-element unordered set, is given. It is proved that every lattice generated by a three-element unordered set contains a sublattice isomorphic to onė of the lattices in ℒ moreover, ℒ is the smallest such list.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 21 , Issue 2 , March 1976 , pp. 171 - 178
Copyright
Copyright © Australian Mathematical Society 1976

References

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