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I've been trying to read about partial fraction expansion of rational function.

Is the following statement equivalent to the uniqueness+existence of partial function expansion?:

Let $\mathbb{F}$ be an algebraically closed field and let $D=\{\frac{p}{q}~:~p,q\in\mathbb{F}[x],~\deg(p)\leq\deg(q)\}$. Consider $D$ as a linear space above $\mathbb{F}$. Then the set $\{(x-a)^{n}~:~a\in\mathbb{F},~n\leq0\}$ is a basis for $D$.

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Yes. ${}{}{}{}$ – Qiaochu Yuan Jul 5 '12 at 14:14
We tend to say "as a vector space over $\mathbb F$" rather than "as a linear space above $\mathbb F$." But yes, this is correct. – Thomas Andrews Jul 5 '12 at 14:45

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