Prime spectra of lattice-ordered Abelian groups

We prove that for each l-group G, the topological space Spec(G) satisfies a condition Id omega. Generalising a previous construction of Delzell and Ma dden we show that for each nondenumerable cardinal there is a completely no rmal spectral space that is not homeomorphic to Spec(G) for any L-group G. We show also that a stronger form of property Id omega, called Id, suffices to ensure that a completely normal spectral space is homeomorphic to Spec( G) for some l-group G. (C) 1999 Elsevier Science B.V. All rights reserved.