A representation theorem revisited

• Autores: D.G. Johnson
• Localización: Algebra universalis, ISSN 0002-5240, Vol. 56, Nº. 3-4, 2007, págs. 303-314
• Idioma: inglés
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• Resumen

  • In 1962, the author proved that each reduced archimedean f-ring can be represented as an f-ring of continuous extended real-valued function on a locally compact space. The existence of this representation has proved to be quite useful; however, the proof so obscured the definition of the representing functions that deeper applications have remained out of reach. In this paper, we give a new proof of this result; one in which the derivation of the representing functions is more readily accessible. This accessibility is exploited to prove that f-ring homomorphisms on reduced archimedean f-rings are induced by continuous maps between subspaces of their representing spaces, and this leads to further insights into the structure of such homomorphisms.