Embeddings into power series rings

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. LetXΠΔR 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 onXΠΔR. The following are equivalent: (1) τ satisfies the additional condition; for convex subgroups P,Q of T, where (2) There exists a one-to-one homomorphism Γ:T→XΠΔR of ordered rings such that for every convex subgroup Q ofXΠΔR, there exists a convex subgroup P of T such that\(\Gamma (P) \subseteq Q\) and\(\Gamma (\tau (P)) \subseteq \chi (Q)\).