Countable chains of distributive lattices as maximal semilattice quotients of positive cones of dimension groups
Pavel Růžička · Czech digital mathematics library · 2006
We study the question whether a direct limit of a countable chain of distributive lattices with zero and zero-preserving join-homomorphisms can be represented as the maximal semilattice quotient of the positive cone of a dimension group. We answer the question in a#rmative in case the sizes of the lattices are at most 1 and we find a counter-example of size 2 , where a is a certain cardinal invariant satisfying 2 # 0 .