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Let a be a saturated ideal of O(R n ) and Y R n the germ of the support of the coherent sheaf that extends aO R n to a suitable complex open neighborhood of R n . We study the relationship between a normal primary decomposition of a and the decomposition of Y R n as the union of its irreducible components. If a := p is prime, then I(Z(p)) = p if and only if the (complex) dimension of Y R n coincides with the (real) dimension of Z(p).doi:10.1090/tran/6436 fatcat:fuzatja7dnhqjdh7n42ue5iajy