Startseite Mathematik Confluence and combinatorics in finitely generated unital lattice-ordered abelian groups
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Confluence and combinatorics in finitely generated unital lattice-ordered abelian groups

  • Manuela Busaniche EMAIL logo , Leonardo Cabrer und Daniele Mundici
Veröffentlicht/Copyright: 25. Februar 2012
Forum Mathematicum
Aus der Zeitschrift Band 24 Heft 2

Abstract.

A unital -group (G,u) is an abelian group G equipped with a translation-invariant lattice-order and a distinguished element u, called order-unit, whose positive integer multiples eventually dominate each element of G. It is shown that, for direct systems and of finitely presented unital -groups, confluence is a necessary condition for limlim. (Sufficiency is an easy byproduct of a general result). When (G,u) is finitely generated we equip it with a sequence (G,u)=(W0,W1,...) of weighted abstract simplicial complexes, where Wt+1 is obtained from Wt either by the classical Alexander binary stellar operation, or by deleting a maximal simplex of Wt. We show that the map (G,u)(G,u) has an inverse. A confluence criterion is given to recognize when two sequences arise from isomorphic unital -groups.

Keywords.: Lattice-ordered abelian group; rational polyhedron; order-unit; confluence; direct system; confluent direct system; simplicial complex; abstract simplicial complex; weighted abstract simplicial complex; stellar subdivision; Alexander starring; regular fan; De Concini–Procesi theorem; piecewise linear function; Elliott classification; AF
Received: 2009-08-19
Revised: 2010-02-19
Published Online: 2012-02-25
Published in Print: 2012-March

© 2012 by Walter de Gruyter Berlin Boston

Artikel in diesem Heft

  1. Masthead
  2. Uniform weighted estimates for oscillatory singular integrals
  3. Solutions of the linear Boltzmann equation and some Dirichlet series
  4. Confluence and combinatorics in finitely generated unital lattice-ordered abelian groups
  5. Periodic flat resolutions and periodicity in group (co)homology
  6. Precompact noncompact reflexive Abelian groups
  7. Free profinite p-rings
  8. Cellular covers for R-modules and varieties of groups
  9. Time changes of local Dirichlet spaces by energy measures of harmonic functions
  10. A construction of a universal connection
  11. Finitely generated algebraic structures with various divisibility conditions
  12. Quasiprojective varieties admitting Zariski dense entire holomorphic curves
  13. Conservativeness of non-symmetric diffusion processes generated by perturbed divergence forms
https://doi.org/10.1515/form.2011.059
Schlagwörter für diesen Artikel
Lattice-ordered abelian group; rational polyhedron; order-unit; confluence; direct system; confluent direct system; simplicial complex; abstract simplicial complex; weighted abstract simplicial complex; stellar subdivision; Alexander starring; regular fan; De Concini–Procesi theorem; piecewise linear function; Elliott classification; AF

Artikel in diesem Heft

  1. Masthead
  2. Uniform weighted estimates for oscillatory singular integrals
  3. Solutions of the linear Boltzmann equation and some Dirichlet series
  4. Confluence and combinatorics in finitely generated unital lattice-ordered abelian groups
  5. Periodic flat resolutions and periodicity in group (co)homology
  6. Precompact noncompact reflexive Abelian groups
  7. Free profinite p-rings
  8. Cellular covers for R-modules and varieties of groups
  9. Time changes of local Dirichlet spaces by energy measures of harmonic functions
  10. A construction of a universal connection
  11. Finitely generated algebraic structures with various divisibility conditions
  12. Quasiprojective varieties admitting Zariski dense entire holomorphic curves
  13. Conservativeness of non-symmetric diffusion processes generated by perturbed divergence forms
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