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On the Riesz structures of a lattice ordered abelian group

In: Mathematica Slovaca, vol. 69, no. 6
Giacomo Lenzi

Details:

Year, pages: 2019, 1237 - 1244
Keywords:
lattice ordered abelian group, Riesz space, strong unit, partial isomorphism, MV-algebra, Riesz MV-al\-gebra fixed point
About article:
A Riesz structure on a lattice ordered abelian group $G$ is a real vector space structure where the product of a positive element of $G$ and a positive real is positive. In this paper we show that for every cardinal $k$ there is a totally ordered abelian group with at least $k$ Riesz structures, all of them isomorphic. Moreover two Riesz structures on the same totally ordered group are partially isomorphic in the sense of model theory. Further, as a main result, we build two nonisomorphic Riesz structures on the same l-group with strong unit. This gives a solution to a problem posed by Conrad in 1975. Finally we apply the main result to MV-algebras and Riesz MV-algebras.
How to cite:
ISO 690:
Lenzi, G. 2019. On the Riesz structures of a lattice ordered abelian group. In Mathematica Slovaca, vol. 69, no.6, pp. 1237-1244. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0304

APA:
Lenzi, G. (2019). On the Riesz structures of a lattice ordered abelian group. Mathematica Slovaca, 69(6), 1237-1244. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0304
About edition:
Publisher: Mathematical Institute, Slovak Academy of Sciences, Bratislava
Published: 22. 12. 2019