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Embeddings into power series rings

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Abstract

Let T be an ordered ring without divisors of zero, and letA be the set of archimedean subgroups of T generated by a Banaschewski functionτ. LetXΠΔ R be the power series ring of the real numbers ℝ over the totally ordered semigroup Δ of archimedean classes of T, and letχ be the usual Banaschewski function onXΠΔ R. The following are equivalent:

  1. (1)

    τ satisfies the additional condition; for convex subgroups P,Q of T,

    where

  2. (2)

    There exists a one-to-one homomorphism Γ:T→XΠΔ R of ordered rings such that for every convex subgroup Q ofXΠΔ R, there exists a convex subgroup P of T such that\(\Gamma (P) \subseteq Q\) and\(\Gamma (\tau (P)) \subseteq \chi (Q)\).

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Author notes

  1. R. H. Redfield

    Present address: Hamilton College, Clinton, 13323, NY, USA

Authors and Affiliations

  1. Simon Fraser University, Burnaby, B. C., Canada

    R. H. Redfield

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  1. R. H. Redfield
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Additional information

This work was done while the author was visiting Simon Fraser University, where he was supported in part by NSERC grant A4044. The author wishes to thank the Department of Mathematics and Statistics at Simon Fraser and, in particular, N.R. Reilly for their hospitality.

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Redfield, R.H. Embeddings into power series rings. Manuscripta Math 56, 247–268 (1986). https://doi.org/10.1007/BF01180767

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  • DOI: https://doi.org/10.1007/BF01180767

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