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Chain conditions on posets
Published online by Cambridge University Press: 18 May 2009
Extract
The aim of this note is to generalize to an arbitrary partially ordered set (poset) (P, ≦) the standard lattice results on the Jordan–Dedekind Chain Condition (abbreviated hereafter to J.D.C.C.). Birkhoff [1] defines semimodularity for a lattice L by
(ξ) if x, y cover a and x # y, then x ∨ y covers x and y.
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- Copyright © Glasgow Mathematical Journal Trust 1974