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(9) Consider the substitution homomorphism given by My (Peas) = p (6₂) (You can assume it's a homonoephium) M: 2[^) -> 2 [r] (a) Show M₂ is onto (6) Determine Kerfly Prove your claim. (c) Is Kerl, Prime, Meximel or neither? Why Kerlly and

(9) Consider the substitution homomorphism given by My (Peas) = p (6₂) (You can assume it's a homonoephium) M: 2[^) -> 2 [r] (a) Show M₂ is onto (6) Determine Kerfly Prove your claim. (c) Is Kerl, Prime, Meximel or neither? Why Kerlly and

Advanced Engineering Mathematics
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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**Consider the Substitution Homomorphism** Given the homomorphism \( M_{t_2} : \mathbb{Z}[x] \to \mathbb{Z}(t_2) \) defined by \( M_{t_2}(p(x)) = p(t_2) \). (You can assume it's a homomorphism.) (a) Show \( M_{t_2} \) is onto. (b) Determine \( \text{Ker } M_{t_2} \) and prove your claim. (c) Is \( \text{Ker } M_{t_2} \) prime, maximal, or neither? Why?
Transcribed Image Text:**Consider the Substitution Homomorphism** Given the homomorphism \( M_{t_2} : \mathbb{Z}[x] \to \mathbb{Z}(t_2) \) defined by \( M_{t_2}(p(x)) = p(t_2) \). (You can assume it's a homomorphism.) (a) Show \( M_{t_2} \) is onto. (b) Determine \( \text{Ker } M_{t_2} \) and prove your claim. (c) Is \( \text{Ker } M_{t_2} \) prime, maximal, or neither? Why?
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