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Real holomorphy rings and the complete real spectrum

D. GondardM. Marshall — 2010

Annales de la faculté des sciences de Toulouse Mathématiques

The complete real spectrum of a commutative ring A with 1 is introduced. Points of the complete real spectrum Sper c A are triples α = ( 𝔭 , v , P ) , where 𝔭 is a real prime of A , v is a real valuation of the field k ( 𝔭 ) : = qf ( A / 𝔭 ) and P is an ordering of the residue field of v . Sper c A is shown to have the structure of a spectral space in the sense of Hochster []. The specialization relation on Sper c A is considered. Special attention is paid to the case where the ring A in question is a real holomorphy ring.

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