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Planar Sublattices of a Free Lattice. I

Published online by Cambridge University Press:  20 November 2018

Ivan Rival  and
Bill Sands
Ivan Rival
Affiliation:
University of Calgary, Calgary, Alberta
Bill Sands
Affiliation:
University of Manitoba, Winnipeg, Manitoba.
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There are three lattice-theoretic properties that are generally used to open a discussion on sublattices of a free lattice:

(W) for all a, b, c, d, a Λ b ≦ c V d implies a A b ≦ c, a Λ b g rf, a ≦cVd,orb ≦ c V d;

(SDv) for all a, b, c, a V b = a V c implies a V b = a V (b Λ c ) ;

(SDΛ) for all a, b, c, a Λ b = a Λ c implies a Λ b = a Λ (b V c).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 30 , Issue 6 , 01 December 1978 , pp. 1256 - 1283
Copyright
Copyright © Canadian Mathematical Society 1978

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