Let R= Z/5Z, the integers mod 5. The ring of Gaussian integers mod 5 is defined by R[i] = {a+ bi : a, be Z/5Z and i=-1}. Show that R[i} is not an integral domain (and hence not a field) by showing that 3+i is a zero-divisor in R[i].

Let R= Z/5Z, the integers mod 5. The ring of Gaussian integers mod 5 is defined by R[i] = {a+ bi : a, be Z/5Z and i=-1}. Show that R[i} is not an integral domain (and hence not a field) by showing that 3+i is a zero-divisor in R[i].

Name: Q8 Let R= Z/5Z, the integers mod 5. The ring of Gaussian integers mod
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Description: Q8 Let R= Z/5Z, the integers mod 5. The ring of Gaussian integers mod 5 is definedby R[i] = {a+ bi : a, be Z/5Z and i=-1}. Show that R[i} is not an integraldomain (and hence not a field) by showing that 3+i is a zero-divisor in R[i].

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter6: More On Rings

Section6.3: The Characteristic Of A Ring

Problem 4E

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