  Coste and Roy in 1979 defined a structural sheaf on the real Zariski spectrum
of a semi-real ring $A$ and asked whether the ring of the global sections is
$\sum^{-1}_1 A$ where $\sum_1$ is the multiplicative subset $\{1+\sum_{i=1}^n
a_i^2|a_i\in A, n\in N\}$ of $A$. We give a positive answer to this question
for real rings and integral domains.

Algebraic Geometry