RT info:eu-repo/semantics/article
T1 Simple Riesz groups of rank one having wild intervals
A1 Ortus, F.
A1 Pardo, E.
A1 Perera, F.
A2 Matemáticas
K1 Simple Riesz group
K1 Interval
K1 C*C*-algebra of real rank zero
AB 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(Dn)n⩾1 and D , that satisfy: (a) for each n⩾1n⩾1, tDn≠G+tDn≠G+ for every (t