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Distributive Sublattices of a Free Lattice

Published online by Cambridge University Press:  20 November 2018

Fred Galvin
Affiliation:
University of Minnesota
Bjarni Jónsson
Affiliation:
University of Minnesota
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The purpose of this note is to characterize those distributive lattices that can be isomorphically embedded in free lattices. If it is known (cf. (2)) that in a free lattice every element is either additively or multiplicatively irreducible, and consequently every sublattice of a free lattice must also have this property. We therefore begin by studying the class of all those distributive lattices in which this condition is satisfied.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1961

References

1. Jónsson, B., Sublattices of a free lattice. Can. J. Math., 13 (1961), 256264.Google Scholar
2. Whitman, P. M., Free lattices I, Ann. Math. (2), 42 (1941), 325330.Google Scholar