Dilworth’s Work on Decompositions in Semimodular Lattices
Bjàrni Jónsson · Birkhäuser Boston eBooks · 1990
In a series of papers written over a period of twenty years, the first one appearing in 1940, Dilworth investigated representations of an element a in a complete lattice as a meet a = ∧ Q of a set Q of completely meet irreducible elements. For brevity we refer to such a representation, or to the set Q itself, as a decomposition of a . The decomposition is said to be irredundant if no proper subset of Q is a decomposition of a . The survey paper [9] by Dilworth provides an excellent summary of the principal results obtained.