Epimorphism from Polynomial Forms to Polynomial Functions
From ProofWiki
Theorem
Let $D$ be an integral domain.
Let $D \left[{X}\right]$ be the ring of polynomial forms in $X$ over $D$.
Let $P \left({D}\right)$ be the ring of polynomial functions over $D$.
The mapping $\kappa: D \left[{X}\right] \to P \left({D}\right)$ given by $\displaystyle \kappa \left({\sum_{k=0}^n {a_k \circ X^k}}\right) = f$
where $\displaystyle f = \sum_{k=0}^n {a_k \circ x^k}, x \in D$
is a ring epimorphism.
Proof
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