Real reduced multirings and multifields

@inproceedings{Marshall2006RealRM,
  title={Real reduced multirings and multifields},
  author={Murray Marshall},
  year={2006}
}
We work in the big category of commutative multirings with 1. A multiring is just a ring with multivalued addition. We show that certain key results in real algebra (parts of the Artin-Schreier theory for fields and the Positivstellensatz for rings) extend to the corresponding objects in this category. We also show how the space of signs functor A Ã Qred(A) defined in [1] and [7] extends to this category. The proofs are no more difficult than in the ring case. In fact they are easier. This… CONTINUE READING
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