# Let R be a commutative ring. Show that R[x] has a subring isomorphic to R.

Let R be a commutative ring. Show that R[x] has a subring isomorphic to R.
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joshyoung05M
Let R be a commutative rng and consider R[x]
Define: $\varphi :R\to R\left[x\right]$ by $r↦r$
Here, clearly we can say that $\varphi$ is one-to-one and homomorphism
Now, $\varphi \left(R\right)$ is subsring of R[x] since it is the imag of a homomorphism
Then $\varphi \left(R\right)$ is subsring of R[x] isomorphic to R