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Distributive Sublattices of a Free Lattice

Published online by Cambridge University Press:  20 November 2018

Fred Galvin  and
Bjarni Jónsson
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
Information
Canadian Journal of Mathematics , Volume 13 , 1961 , pp. 265 - 272
Copyright
Copyright © Canadian Mathematical Society 1961

References

1. Jónsson, B., Sublattices of a free lattice. Can. J. Math., 13 (1961), 256–264.Google Scholar
2. Whitman, P. M., Free lattices I, Ann. Math. (2), 42 (1941), 325–330.Google Scholar