Answered: Let R = Z/3Z, the integers mod 3. The…

Let R = Z/3Z, the integers mod 3. The ring of Gaussian integers mod 3 is defined by R[i] = { a + bi : a,b e Z/3Z and i = sqrt(-1)}

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 18E: Let a0 in the ring of integers . Find b such that ab but (a)=(b).

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Question

Let R = Z/3Z, the integers mod 3. The ring of Gaussian integers mod 3 is defined by R[i] = { a + bi : a,b e Z/3Z and i = sqrt(-1)}. Show that R[i] is a field.

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