Denote by Zm = {[0]m [1]m,..., [m - 1]m} the ring of integers modulo m. Consider the rings R = Z24 and S = Z4 × Z6. Let 0 RS be the map defined by ([x]24) = ([x]4, [4x]6). (b) Is a homomorphism of rings? Explain.
Denote by Zm = {[0]m [1]m,..., [m - 1]m} the ring of integers modulo m. Consider the rings R = Z24 and S = Z4 × Z6. Let 0 RS be the map defined by ([x]24) = ([x]4, [4x]6). (b) Is a homomorphism of rings? Explain.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter6: More On Rings
Section6.2: Ring Homomorphisms
Problem 28E
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![Denote by Zm = {[0]m [1]m,..., [m - 1]m} the ring of integers modulo m.
Consider the rings R = Z24 and S = Z4 × Z6. Let 0 RS be the map
defined by ([x]24) = ([x]4, [4x]6).
(b) Is a homomorphism of rings? Explain.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0de9773e-39c1-4df6-a7d6-864501c7f552%2F34c4e68b-f03a-4cb9-b7b0-6389f422f2c7%2Fn77c9ca_processed.png&w=3840&q=75)
Transcribed Image Text:Denote by Zm = {[0]m [1]m,..., [m - 1]m} the ring of integers modulo m.
Consider the rings R = Z24 and S = Z4 × Z6. Let 0 RS be the map
defined by ([x]24) = ([x]4, [4x]6).
(b) Is a homomorphism of rings? Explain.
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