Classes of Ultrasimplicial Lattice-Ordered Abelian Groups

A lattice-ordered abelian group is called ultrasimplicial iff every finite set of positive elements belongs to the monoid generated by some finite set of positiveZ-independent elements. This property originates from Elliottʹs classification of AFC*-algebras. Using fans and their desingularizations, it is proved that the ultrasimplicial property holds for everyn-generated archimedeanl-group whose maximall-ideals of ranknare dense. As a corollary we obtain simpler proofs of results, respectively by Elliott and by the present author, stating that totally ordered abelian groups, as well as freel-groups, are ultrasimplicial.