polynomial rings in R[x]

sombra · **Joined:** Mon, 20 Oct 2008 00:45:03 UTC **Posts:** 18

R is a ring and I an ideal. If R[x] and I[x] are polynomial rings in x over R and I respectively how do I show:
I[x] is an ideal of R[x]
and
R[x]/I[x] isomorphic to (R/I)[x]?

Shadow · **Posted:** Tue, 4 Nov 2008 06:43:32 UTC

Use the definition of an ideal and the fact that

is an

-ideal.

For the second one, use the natural ring homomorphism, $\pi:R[x]\rightarrow (R/I)[x]$ and find the kernel

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polynomial rings in R[x]

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