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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.2012-11-17

2 Answers 2

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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.2012-11-17
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Hint $ $ The evaluation hom $\rm\:f(x)\to f(0)\:$ is $1$-$1$, onto, restricted to polynomials of degree zero.

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    @MUH the claim is *restricted* to polynomials of degree zero (constants).2016-06-29