?-group homomorphisms between reduced archimedean f-rings |
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Authors: | Karim Boulabiar Anthony Hager |
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Institution: | (1) Department of Mathematics, Wesleyan University, Middletown, CT 06457, USA;(2) 5 W. Oak St., Ramsey, NJ 07446, USA |
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Abstract: | Let A and B be reduced archimedean f-rings, A with identity e; let $A\,\mathop \to \limits^\gamma\,BLet A and B be reduced archimedean f-rings, A with identity e; let
A \mathop ? g BA\,\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 ? r B (w)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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Keywords: | |
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