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Every Abelian ℓ-Group is Ultrasimplicial

✍ Scribed by Vincenzo Marra

Book ID
102576294
Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
114 KB
Volume
225
Category
Article
ISSN
0021-8693

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✦ Synopsis

A partially ordered abelian group G is said to be ultrasimplicial if for every finite set P of positive elements of G there is a finite set B of positive elements which are linearly independent in the Z-module G, and such that P belongs to the monoid generated by B. In this paper we prove the result stated in the title.

📜 SIMILAR VOLUMES

Classes of Ultrasimplicial Lattice-Order
Classes of Ultrasimplicial Lattice-Ordered Abelian Groups
✍ Daniele Mundici 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 71 KB

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 desingularizatio