Let p be a prime number. Let Z(p) be the following subset of Q: a where a € Z, b E N, such that p does not divide b}. b' Z(p) = (a) Show that Z(p) is a ring (under operations of addition and multiplication of rational numbers). (b) Show that the ideal (p) of Z(p) generated by p is a maximal ideal.

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Q: (10) is maxi

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

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A: Ideal of a ring