(b) U = {q(x) € Z3 [x] : x²+x+1 is a factor of q(x)} in Z3 [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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How do I check if b) is an ideal? I think it is principal and prime so it must be an ideal but I don't think it's maximal since it's reducible?
Thank you very much for the help!!
![Question 3 In each of the following cases, check whether the given subset is (1) an ideal, (2)
a maximal ideal, (3) a principal ideal, and (4) a prime ideal. Justify your answer.
(a) I = {0,2} in Z4.
(b) U = {q(x) ≤ Z3[x] : x² +x+ 1 is a factor of q(x)} in Z3 [x].
E
(c) J = {a+i·b: 17a – 190a²b² > 0} in Q(i) = {a+i⋅ b : a,b ≤ Q}, where i E C is the
imaginary unit (i² = −1).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F138da6ab-7efa-4b8c-b154-28405afcc8c9%2F6e74c3ca-1a3d-4bd0-ba4b-8a58d9db25e2%2F11qq8hs_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Question 3 In each of the following cases, check whether the given subset is (1) an ideal, (2)
a maximal ideal, (3) a principal ideal, and (4) a prime ideal. Justify your answer.
(a) I = {0,2} in Z4.
(b) U = {q(x) ≤ Z3[x] : x² +x+ 1 is a factor of q(x)} in Z3 [x].
E
(c) J = {a+i·b: 17a – 190a²b² > 0} in Q(i) = {a+i⋅ b : a,b ≤ Q}, where i E C is the
imaginary unit (i² = −1).
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