Ordinal Sums Of Projectives In Varieties Of Lattices

28.47> be a subset. Then every element of FV (Z) is either below W Y or above V (Z - Y). Proof. If V is the trivial variety then the result is clear. Otherwise the result follows from examining the homomorphism from FV (X) to 2 which maps the elements of Y to 0 and the other generators to 1. For w # FV (X) define the rank of w, denote r(w), to be the the least integer k such that there is a term of length k representing w. For Y a finite subset of X, let # Y be the endomorphism of FV (X) extending the map on X: # Y (z) =<