### Abstract

We prove that every partially ordered simple group of rank one which is not Riesz embeds into a simple Riesz group of rank one if and only if it is not isomorphic to the additive group of the rationals. Using this result, we construct examples of simple Riesz groups of rank one G, containing unbounded intervals (Dn)n≥1 and D, that satisfy: (a) for each n ≥ 1, tDn ≠ G+ for every (t < qn), but qn Dn = D+ (where (qn) is a sequence of relatively prime integers); (b) for every n ≥ 1, nD ≠ G+. We sketch some potential applications of these results in the context of K-theory. © 2004 Elsevier Inc. All rights reserved.

Original language | English |
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Pages (from-to) | 111-140 |

Journal | Journal of Algebra |

Volume | 284 |

DOIs | |

Publication status | Published - 1 Feb 2005 |

### Keywords

- -algebra of real rank zero
- Interval: C
- Simple Riesz group

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## Cite this

Ortus, F., Pardo, E., & Perera, F. (2005). Simple Riesz groups of rank one having wild intervals.

*Journal of Algebra*,*284*, 111-140. https://doi.org/10.1016/j.jalgebra.2004.10.002