Show that I = Z × {0} × ZL = {(a,0, b) : a,b E Z} is a prime ideal of R = Z × Z × Z but it is not its maximal ideal. (Don't show that I is an ideal of R.)

Q: Let S = {0, 2, 4, 6, 8} CZ10. Is S an ideal of Z10?

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Q: Let S = {a + bi : a, b e Z, b is even}. Then S is %3D not an ideal of Z[i] an ideal of Z[i]

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Q: Prove that I = is not a prime ideal of Z[i].

A: Solution :-

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Q: Prove that the ideal in Q[x] is maximal.

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Q: Let S = {a+bi: a, b € Z and b is even}. Is S an ideal of Z[i]?

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Q: Let I = {(a, 0) | a e Z}. Show that I is a prime ideal, but not a maximal ideal of the ring Z×Z.

A: Ideal of a ring

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Q: def mx {fe Fun(X, R): f(x)=0}. (i) Prove that my is a maximal ideal in Fun(X, R). (ii) Prove that…

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