Abstract
Let A and B be reduced archimedean f-rings, A with identity e; let \(A\,\mathop \to \limits^\gamma\,B\) be an ℓ-group homomorphism, and set w = γ (e). We show (with some vagaries of phrasing here) (1) γ = w·ρ for a canonical ℓ-ring homomorphism \(A\,\mathop \to \limits^\rho\,B (w)\), where B (w) is an extension of B in which w is a von Neumann regular element, and (2) for X A ,X B canonical representation spaces for A, B, γ is realized via composition with a unique partially defined continuous function from X B to X A .
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Presented by M. Henriksen.
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Boulabiar, K., Hager, A. ℓ-group homomorphisms between reduced archimedean f-rings. Algebra Univers. 62, 329–337 (2009). https://doi.org/10.1007/s00012-010-0031-1
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DOI: https://doi.org/10.1007/s00012-010-0031-1