How can I show that c) is an Ideal? I know that it is not maximal, prime and principal but I'm not sure how exactly I can show that it is an Ideal 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].(c) J = {a+i.b: 17a – 190a²b² > 0} in Q(i) = {a+i·b : a,b € Q}, where i EC is theimaginary unit (i² = −1).

To determine whether the subset J = {a + ib : 17a - 190a2b2 > 0} in Q(i) = {a + ib : a, b ∈ Q} is…

Answered: Question 3 In each of the following…

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 16E

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