Abstract
In this work we prove that the ringR[V] of an affine or projective real variety V is factorial if and only if the codimension 1 irreductible subvarieties of V are complete intersections. In particular ifR[V] is integrally closed, the divisor class group Cl (V) of the variety V is generated by the classes of the (homogeneous) real prime ideals ofR[V].
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