Finitely presented lattice-ordered abelian groups with order-unit

JOURNAL OF ALGEBRA

卷:343

Article

Cabrer, Leonardo²  Mundici, Daniele¹ 

[1] Univ Florence, Dipartimento Matemat Ulisse Dini, I-50134 Florence, Italy

[2] Univ Nacl Ctr, Fac Ciencias Exactas, Dept Matemat, RA-7000 Tandil, Argentina

关键词: Lattice-ordered abelian group;    Order-unit;    Spectral space;    Basis;    Schauder basis;    Dimension group;    Elliott classification;    Simplicial group;    Finite presentation;    Projective;    Rational polyhedron;    Simplicial complex;    Unimodular triangulation;    Fan;   

DOI  :  10.1016/j.jalgebra.2011.07.007

来源: Elsevier

【 摘 要 】

Let G be an l-group (which is short for lattice-ordered abelian group). Baker and Beynon proved that G is finitely presented iff it is finitely generated and projective. In the category U of unital l-groups, those l-groups having a distinguished order-unit u, only the (double left arrow)-direction holds in general. We show that a unital l-group (G, u) is finitely presented iff it has a basis. A large class of projectives is constructed from bases having special properties. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free