Expanding lattice ordered abelian groups to Riesz spaces

Authors

DOI:

https://doi.org/10.1515/ms-2022-0001

Keywords:

Abelian lattice ordered group, Riesz space, MV-algebra, Riesz MV-algebra

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.

Author Biographies

Antonio Di Nola, University of Salerno

Department of Mathematics
University of Salerno
Via Giovanni Paolo II 132
84084 Fisciano
ITALY

Giacomo Lenzi, University of Salerno

Department of Mathematics
University of Salerno
Via Giovanni Paolo II 132
84084 Fisciano
ITALY

Gaetano Vitale, University of Salerno

Department of Mathematics
University of Salerno
Via Giovanni Paolo II 132
84084 Fisciano
ITALY

Published

2022-02-16

Issue

Section

Articles - Other topics