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: Suppose z is implicitly given as a function of x and y, according to The equation: y−zx3=1−yz2 The…

A: Suppose z is implicitly given as a function of x and y, according to The equation: y−zx3=1−yz2 The…

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Q: 3. In the ring (Z,2, +12,-12 ), the following ideal is maximal ........ (а) (2) (b) (3) (c) (a) and…

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Q: et J be the ideal of R = Cla, b, c, d] generated by a²b, b³c, cd, d5 a. a) Write A = V(J) as a union…

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Q: 4. Consider P = P(3, V15) = {a + b/15|a, be Z, 3|a} and Z[V15] = {a + bv15|a, b e Z}. (a) Prove that…

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A: Ideal of a ring

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Q: Prove that if (I,+,) is an ideal of the ring (R,+, ), then rad I In rad R. %3D

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