Polynomial Ring is Generated by Indeterminate over Ground Ring

From ProofWiki
Jump to navigation Jump to search

Theorem

Let $R$ be a commutative ring with unity.

Let $R \sqbrk X$ be a polynomial ring over $R$.

Let $\iota: R \to R \sqbrk X$ be the embedding.


Then $R \sqbrk X$ is generated by $X$ over $R$.


Proof