If ø is a ring homomorphism from R to S. Then i. ii. Prove that (kero) is an ideal of S. Prove that o'Imø) is an ideal of R.
If ø is a ring homomorphism from R to S. Then i. ii. Prove that (kero) is an ideal of S. Prove that o'Imø) is an ideal of R.
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 8E: Exercises
If and are two ideals of the ring , prove that the set
is an ideal of that contains...
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![If ø is a ring homomorphism from R to S. Then
Prove that (ker o) is an ideal of S.
i.
Prove that o(Imø) is an ideal of R.
Explain (i) and (ii) also with an example.
ii.
iii.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F78a061f0-3133-4d1e-a377-2274ae596e8d%2F70ae374e-86f9-4ac0-b788-f28ec77be4fc%2Fjcqeuq7_processed.jpeg&w=3840&q=75)
Transcribed Image Text:If ø is a ring homomorphism from R to S. Then
Prove that (ker o) is an ideal of S.
i.
Prove that o(Imø) is an ideal of R.
Explain (i) and (ii) also with an example.
ii.
iii.
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