2. (a) Let de Z\ {0, 1} be square-free. Let a € Z[√] \ {0} and assume that N(a)is a prime number. Show that a is an irreducible element of Z[√].(b) Hence find an irreducible element of Z[2] which is not real.

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Answered: 2. (a) Let de Z\ {0, 1} be square-free.…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter8: Polynomials

Section8.4: Zeros Of A Polynomial

Problem 19E

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2. (a) Let de Z\ {0, 1} be square-free. Let a € Z[√] \ {0} and assume that N(a) is a prime number. Show that a is an irreducible element of Z[√]. (b) Hence find an irreducible element of Z[2] which is not real.