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Forum Mathematicum

Managing Editor: Bruinier, Jan Hendrik

Ed. by Cohen, Frederick R. / Droste, Manfred / Darmon, Henri / Duzaar, Frank / Echterhoff, Siegfried / Gordina, Maria / Neeb, Karl-Hermann / Shahidi, Freydoon / Sogge, Christopher D. / Takayama, Shigeharu / Wienhard, Anna

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Volume 27, Issue 3


Simplicial geometry of unital lattice-ordered abelian groups

Leonardo Manuel Cabrer
  • Departamento de Matemática, Facultad de Ciencias Exactas, Universidad Nacional del Centro de la Provincia de Buenos Aires, Pinto 399, Tandil (7000), Argentina
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Published Online: 2013-03-07 | DOI: https://doi.org/10.1515/forum-2011-0131


By a unital ℓ-group we mean a lattice-ordered abelian group with a distinguished order unit. This paper is concerned with the category 𝖴fp of finitely presented unital ℓ-groups. Using the duality between 𝖴fp and a category of rational polyhedra, we will provide (i) a construction of finite limits and co-limits in 𝖴fp; (ii) a Cantor–Bernstein–Schröder theorem for finitely presented unital ℓ-groups; (iii) a proof that the fibered product of finitely generated projective unital ℓ-groups is projective; (iv) a geometrical characterization of exact unital ℓ-groups.

Keywords: Unital lattice-ordered group; finitely presented; rational polyhedron; exact formula; projective algebra

MSC: 06F20; 52B20; 18B30; 05E45; 52B11; 18A35; 55U05; 55U10; 57Q05

About the article

Received: 2011-11-14

Revised: 2012-08-19

Published Online: 2013-03-07

Published in Print: 2015-05-01

Citation Information: Forum Mathematicum, Volume 27, Issue 3, Pages 1309–1344, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/forum-2011-0131.

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