Finitely presented lattice-ordered abelian groups with order-unit

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.