Let p be a prime number. Let Z(p) be the following subset of Q:aZ(p) = {2, where a € Z,b ≤ N, such that p does not divide b}.b'(a) Show that Z(p) is a ring (under operations of addition and multiplicationof rational numbers).(b) Show that the ideal (p) of Z(p) generated by p is a maximal ideal.

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Answered: Let p be a prime number. Let Z(p) be…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter6: More On Rings

Section6.1: Ideals And Quotient Rings

Problem 9E: Find the principal ideal (z) of Z such that each of the following sums as defined in Exercise 8 is...

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