Abstract
Let I be the graded ring of homogeneous rational polynomials in n-variables which are numerical over Z. Then I is a subring of Γ, the divided polynomial algebra over Z in the n-variables. A consequence of the main theorem is that for any positive integer k, the image of the induced homomorphism I⊗(Z/kZ) → Γ ⊗ (Z/kZ) is a finite graded ring.
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