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First we prove a statement in a paper of Paul Conrad (given without proof) that every non-archimedean totally ordered abelian group has at least two Riesz space structures, if any. Then, as a main result, we prove that there is a non-archimedean lattice ordered abelian group with strong unit having only one Riesz space structure. This gives a solution to a problem posed in a paper of Conrad dating back to 1975. Then we combine these results and the categorial equivalence between lattice ordered abelian groups with strong unit and MV-algebras (due to Daniele Mundici) and the one between Riesz spaces with strong unit and Riesz MV-algebras (due to Di Nola and Ioana Leustean). By combining these tools, we prove that every non-semisimple totally ordered MV-algebra has at least two Riesz MV-algebra structures, if any, and that there is a non-semisimple MV-algebra with only one Riesz MV-algebra structure.<\/jats:p>","DOI":"10.1007\/s11083-024-09662-0","type":"journal-article","created":{"date-parts":[[2024,3,6]],"date-time":"2024-03-06T10:02:26Z","timestamp":1709719346000},"page":"787-797","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On a Problem of Conrad on Riesz Space Structures"],"prefix":"10.1007","volume":"41","author":[{"given":"Giacomo","family":"Lenzi","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,3,6]]},"reference":[{"key":"9662_CR1","doi-asserted-by":"crossref","unstructured":"Aliprantis, C.D., Burkinshaw, O.: Locally solid Riesz spaces with applications to economics. No. 105. American Mathematical Soc. 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