I hope the answer is yes. It would suffice to construct a homomorphism to a formally real field. I think it would then suffice to extend the partial order to a total ring order, but I'm not sure if this is possible, nor am I sure if this would actually suffice.
2026-03-26 04:16:05.1774498565
Does every partially ordered commutative ring admit an order preserving homomorphism to a real closed field?
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