Exercise 14.3. Let p be a prime number, and let ø : Z[x] → Zp[x] be the ring homomorphismdefined bynn(Σ a¿x²) := Σ ārx², Vao,.i=0i=0..., an EZ.Here ā¿ € Zp satisfies p | ai – āi. Show that ker(o) is a principal prime ideal.

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Answered: Exercise 14.3. Let p be a prime number,…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter6: More On Rings

Section6.4: Maximal Ideals (optional)

Problem 3E

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Exercise 14.3. Let p be a prime number, and let ø : Z[x] → Zp[x] be the ring homomorphism
defined by
n
n
(Σ a¿x²) := Σ ārx², Vao,.
i=0
i=0
..., an EZ.
Here ā¿ € Zp satisfies p | ai – āi. Show that ker(o) is a principal prime ideal.

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Exercise 14.3. Let p be a prime number, and let ø : Z[x] → Zp[x] be the ring homomorphism defined by n n (Σ a¿x²) := Σ ārx², Vao,. i=0 i=0 ..., an EZ. Here ā¿ € Zp satisfies p | ai – āi. Show that ker(o) is a principal prime ideal.