Archimedean unital groups with finite unit intervals

David J. Foulis

International Journal of Mathematics and Mathematical Sciences, 2003, vol. 2003, 1-15

Abstract:

Let G be a unital group with a finite unit interval E , let n be the number of atoms in E , and let κ be the number of extreme points of the state space Ω ( G ) . We introduce canonical order-preserving group homomorphisms ξ : ℤ n → G and ρ : G → ℤ κ linking G with the simplicial groups ℤ n and ℤ κ .We show that ξ is a surjection and ρ is an injection if and only if G is torsion-free. We give an explicit construction of the universal group (unigroup) for E using the canonical surjection ξ . If G is torsion-free, then the canonical injection ρ is used to show that G is Archimedean if and only if its positive cone is determined by a finite number of homogeneous linear inequalities with integer coefficients.

Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:281017

DOI: 10.1155/S0161171203210395

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