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 positiveZ-independent elements. This property originates from Elliott's classification of AFC-algebras. Using fans and their desingularizations, it is proved that the ultrasimplicial property holds for everyn-generated archimedeanl-group whose maximall-ideals of ranknare 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 freel-groups, are ultrasimplicial.
CLASSES OF ULTRASIMPLICIAL LATTICE-ORDERED ABELIAN GROUPS / D. MUNDICI. - In: JOURNAL OF ALGEBRA. - ISSN 0021-8693. - STAMPA. - 213:(1999), pp. 596-603. [10.1006/jabr.1998.7679]
CLASSES OF ULTRASIMPLICIAL LATTICE-ORDERED ABELIAN GROUPS
MUNDICI, DANIELE
1999
Abstract
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 positiveZ-independent elements. This property originates from Elliott's classification of AFC-algebras. Using fans and their desingularizations, it is proved that the ultrasimplicial property holds for everyn-generated archimedeanl-group whose maximall-ideals of ranknare 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 freel-groups, are ultrasimplicial.
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