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Embedding rank one simple groups into rank one simple Riesz groups

Published online by Cambridge University Press:  26 February 2003

E. Pardo
E. Pardo
Affiliation:
Departamento de Matemáticas, Universidad de Cádiz, Apartado 40, 11510 Puerto Real (Cádiz), Spain e-mail: enrique.pardo@uca.es
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We give a method for embedding a large family of partially ordered simple groups of rank one into simple Riesz groups of rank one. In particular, we answer in the affirmative a question of Wehrung, by constructing a torsion-free, simple Riesz group G of rank one containing an interval D\varsubsetneqq G^+ such that 2D=G^+. We sketch some potential applications of this result in the context of monoids of intervals and K-Theory of rings.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 44 , Issue 3 , September 2002 , pp. 551 - 567
Copyright
2002 Glasgow Mathematical Journal Trust