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Prove that if Rand S are commutative rings, and R "" S, then R[x] "" S[x]
Chapter 34, Problem 34.12(choose chapter or problem)
QUESTION:
Prove that if R and S are commutative rings, and \(R \approx S\), then \(R[x] \approx S[x]\).
Text Transcription:
R approx S
R[x] approx S[x]
Questions & Answers
QUESTION:
Prove that if R and S are commutative rings, and \(R \approx S\), then \(R[x] \approx S[x]\).
Text Transcription:
R approx S
R[x] approx S[x]
ANSWER:Step 1 of 6
Now we will show that F is injective:
Let satisfies
Now which implies that and then
And since f is injective we deduce, so that
Thus,
Therefore, F is injective