Expanding lattice ordered abelian groups to Riesz spaces

Abstract

First we give a necessary and sufficient condition for an Abelian lattice ordered group to allow expansion into a Riesz space (or vector lattice). So we build a totally ordered Abelian group with two non-isomorphic Riesz spatial structures, thus improving a previous document in which the example was an Abelian trellis group not totally ordered. This answers a question raised by Conrad in 1975. We also give a partial solution to another problem considered in the same document. Finally, we apply our results to MV-algebras and Riesz MV-algebras.