Algebra universalis

, Volume 62, Issue 4, pp 329–337 | Cite as

ℓ-group homomorphisms between reduced archimedean f-rings

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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 .

2000 Mathematics Subject Classification

Primary: 06F25 Secondary: 06F15 46E05 46E25 54C30 

Keywords and phrases

ℓ-group f-ring archimedean ℓ-homomorphism von Neumann regular ring of continuous functions 
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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2010

Authors and Affiliations

  1. 1.Ipest, University of November 7 at CarthageLa MarsaTunisia
  2. 2.Department of Mathematics and Computer ScienceWesleyan UniversityMiddletownU.S.A.

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