Finitely presented lattice-ordered abelian groups with order-unit

被引：6
|
作者：
Cabrer, Leonardo [2 ]
Mundici, Daniele [1 ]
机构：
[1] Univ Florence, Dipartimento Matemat Ulisse Dini, I-50134 Florence, Italy
[2] Univ Nacl Ctr, Fac Ciencias Exactas, Dept Matemat, RA-7000 Tandil, Argentina
来源：
JOURNAL OF ALGEBRA | 2011年 / 343卷 / 01期
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; REPRESENTATIONS;
D O I：
10.1016/j.jalgebra.2011.07.007
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
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.
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页码：1 / 10
页数：10
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