Simple Riesz groups of rank one having wild intervals

Identificadores
URI: http://hdl.handle.net/10498/16076
DOI: 10.1016/j.jalgebra.2004.10.002
ISSN: 0021-8693
Files
Statistics
Metrics and citations
Share
Metadata
Show full item recordDate
2005-01-01Department
MatemáticasSource
Journal of Algebra 284 (2005), 111-140Abstract
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<qnt<qn), but qnDn=G+qnDn=G+ (where (qn)(qn) is a sequence of relatively prime integers); (b) for every n⩾1n⩾1, nD≠G+nD≠G+. We sketch some potential applications of these results in the context of K-theory
Subjects
Simple Riesz group; Interval; C*C*-algebra of real rank zeroCollections
- Artículos Científicos [4821]
- Articulos Científicos Matemáticas [161]