Let P be a prime number. Let Zp) be the following subset of Q: a Z(p) = {₁ where a € Z, bЄ N, such that p does not divide b}. b' (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() generated by p is a maximal ideal.

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Q: For any ideal (1, 1.) of the ring (R, 1.), lefine the set V by Vi - {rER " E I for some nEZ4}. %3D…

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A: Ideal of a ring

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Q: Consider the ring R = 2Z and the ideal I = 24Z of R. Use the Second Isomorphism Theorem to list all…

A: Hi! Please refer to the attachment. Thank you!Explanation:4:

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Q: 6. Suppose that (M,+,.) be a maximal ideal of the commutative ring with identity (R, +,.) and x E M,…

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

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Q: 2. Given f is a homomorphism from the ring (R,+, ) onto the ring (R',+', '), prove that a) if (I,+,…

A: Definition: Let I be an ideal of the ring R. I is said to be maximal ideal if there is no…