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Page $117$ of Atiyah, MacDonald's Introduction to Commutative Algebra text has the following theorem. Let $P(M,t)$ denote the Poincare- series of $M$.

• $\textbf{Theorem.}$ $\bigl(\mathsf{Hilbert-Serre}\bigr)$. $P(M,t)$ is a rational function in $t$ of the form $f(t)/\prod_{i=1}^{s} (1-t^{k_i})$, where $f(t) \in \mathbf{Z}[t]$.

This theorem appears in the section of the book called Hilbert-Functions (page 116), so one understands that it could have possibly been discovered by Hilbert.

• But why is the above theorem attributed to Serre? References about when Serre was credited to this the above theorem would be helpful.
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Page $117$ of Atiyah, MacDonald's Introduction to Commutative Algebra text has the following theorem. Let $P(M,t)$ denote the Poincare- series of $M$.

• $\textbf{Theorem.}$ $\bigl(\mathsf{Hilbert-Serre}\bigr)$. $P(M,t)$ is a rational function in $t$ of the form $f(t)/\prod_{i=1}^{s} (1-t^{k_i})$, where $f(t) \in \mathbf{Z}[t]$.

This theorem appears in the section of the book called Hilbert-Functions (page 116), so one understands that it could have possibly been discovered by Hilbert.

• But why is the following theorem attributed to Serre? References about when Serre was credited to this theorem would be helpful.
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# Why is thefollowingthis theorem attributed to Serre?

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