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Classes of Ultrasimplicial Lattice-Ordered Abelian Groups

✍ Scribed by Daniele Mundici

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 71 KB
Volume: 213
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.1998.7679

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✦ Synopsis

A lattice-ordered abelian group is called ultrasimplicial iff every finite set of positive elements belongs to the monoid generated by some finite set of positive Z-independent elements. This property originates from Elliott's classification of AF C U -algebras. Using fans and their desingularizations, it is proved that the ultrasimplicial property holds for every n-generated archimedean l-group whose maximal l-ideals of rank n are dense. As a corollary we obtain simpler proofs of results, respectively by Elliott and by the present author, stating that totally ordered abelian groups, as well as free l-groups, are ultrasimplicial.

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