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 Post subject: polynomial rings in R[x]Posted: Sun, 2 Nov 2008 07:19:16 UTC
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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]?

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 Post subject: Posted: Tue, 4 Nov 2008 06:43:32 UTC
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Joined: Wed, 30 Mar 2005 04:25:14 UTC
Posts: 12102
Location: Austin, TX
Use the definition of an ideal and the fact that is an -ideal.

For the second one, use the natural ring homomorphism, and find the kernel

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