Classification of Finitely Generated Lattice-ordered Abelian Groups with Order-unit
نویسنده
چکیده
A unital l-group (G,u) is an abelian group G equipped with a translation-invariant lattice-order and a distinguished element u, called orderunit, whose positive integer multiples eventually dominate each element of G. We classify finitely generated unital l-groups by sequences W = (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. A simple criterion is given to recognize when two such sequences classify isomorphic unital l-groups. Many properties of the unital lgroup (G, u) can be directly read off from its associated sequence: for instance, the properties of being totally ordered, archimedean, finitely presented, simplicial, free.
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