Show that Z7[x]/(x³ + 2) is a field.
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 5E
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![(2)
Write down a zero divisor in the ring End (Z3 × Z3) (the ring of endomor-
phisms of the abelian group Z3 × Z3).
(3)
Show that Z7[x]/(x³ + 2) is a field.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1c7265f2-9dda-4402-bf47-87522a081370%2F6298447b-11f2-4bf0-9b0a-3da85b7af2de%2Ftdrl3hb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(2)
Write down a zero divisor in the ring End (Z3 × Z3) (the ring of endomor-
phisms of the abelian group Z3 × Z3).
(3)
Show that Z7[x]/(x³ + 2) is a field.
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