Let : R S be a homomorphism of rings, I an ideal in R, and Jan

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Let ∫: R → S be a homomorphism of rings, I an ideal in R, and Jan ideal in S.

(a) ∫^-1(J) is an ideal in R that contains Ker ∫.

(b) If ∫ is an epimorphism, then ∫(I) is an ideal in S. If ∫ is not surjective, ∫(I) need not be an ideal in S.

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Algebra Graduate Texts In Mathematics 73

ISBN: 9780387905181

8th Edition

Authors: Thomas W. Hungerford

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Question Posted: Apr 15, 2023 03:05 AM

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Let : R S be a homomorphism of rings, I an ideal in R, and Jan

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a Let xy 1J and r R We need to show that xy and rx are also in 1J Sinc...View the full answer

Algebra Graduate Texts In Mathematics 73

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