2) Given Gaussian Integers Z[i] and Z[√√-3] Then One of the following is False : a) All numbers 5 & 7& 13 are irreducible elements in Z[√√-3] b) Both 7 & 13 are reducible elements in Z[√-3] and 5 is reducible in Z[i] c) The number 5 is an irreducible element Z[√-3] but 5 is reducible in Z[i]. d) Both 5 &13 are reducible elements in Z[i].
2) Given Gaussian Integers Z[i] and Z[√√-3] Then One of the following is False : a) All numbers 5 & 7& 13 are irreducible elements in Z[√√-3] b) Both 7 & 13 are reducible elements in Z[√-3] and 5 is reducible in Z[i] c) The number 5 is an irreducible element Z[√-3] but 5 is reducible in Z[i]. d) Both 5 &13 are reducible elements in Z[i].
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter6: More On Rings
Section6.4: Maximal Ideals (optional)
Problem 5E
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