Geodesic
A Dimension Theorem for Real Primes
Canadian journal of mathematics, Tome 26 (1974) no. 1, pp. 108-114

Voir la notice de l'article provenant de la source Cambridge University Press

Let k be a real closed field (see § 2 for a definition). Let be an algebraic closure of k. An algebraic set denned over k is, as usual, a subset of (n some integer greater than 0) which is the set of zeros of some polynomials in k[X 1, . . . , X n]. A variety is denned to be an absolutely irreducible algebraic set. We define the real points of an algebraic set X to be the points in X ∩ kn . One can then define X to be real if I(X ∩ kn ) = I(X). (I(X) = the polynomials in k[X 1, . . . , X n] which vanish on X.) 
Dubois, D.; Efroymson, G. A Dimension Theorem for Real Primes. Canadian journal of mathematics, Tome 26 (1974) no. 1, pp. 108-114. doi: 10.4153/CJM-1974-011-5
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