# $R[x]$ has a subring isomorphic to $R$.

Say $R$ is a commutative ring. Does there exists a subring of $R[x]$ that is isomorphic to $R$?

My approach would be to define the subring of $R[x]$ that generates $R$. Any thoughts?

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Constant polynomials. –  Brian M. Scott Nov 17 '12 at 10:23

## 2 Answers

The ring of constant polynomials in $R[x]$ is isomorphic to $R$

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But the crux of the matter is to prove that! See my answer for one easy way. –  Bill Dubuque Nov 17 '12 at 15:35

Hint  The evaluation hom $\rm\:f(x)\to f(0)\:$ is $1$-$1$, onto, restricted to polynomials of degree zero.

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ok. +1 for quick way. –  Amr Nov 17 '12 at 15:53