Polynomial Functions form Submodule of All Functions

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Theorem

Let $K$ be a commutative ring with unity.

Let $K^K$ be the $K$-module mappings $f: K \to K$.

Let $P \left({K}\right) \subseteq K^K$ be the set of all polynomial functions on $K$.


Then $P \left({K}\right)$ is a $K$-submodule of $K^K$.


Proof


Sources