Answered: If R=Z[x] and f(x) = x2 + 1, remain…

If R=Z[x] and f(x) = x2 + 1, remain true, but g(x) =x. How do you prove that in R/I, [g(x)] x [g(x)] = -1R/I I is still the principal ideal generated by f(x)

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

If R=Z[x] and f(x) = x² + 1, remain true, but g(x) =x. How do you prove that in R/I, [g(x)] x [g(x)] = -1_R/I

I is still the principal ideal generated by f(x)

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