19. Prove: an ideal (I,+, ) of (R, +, ) is the intersection of prime ideals if andonly if a? e I implics a E I. [Ilint: For cach a 4 I, there is a prime ideal (P, +, )

Answered: Image /qna-images/answer/01ca398e-5d19-4e4f-ab7d-30158d38f024.jpg

Answered: and Prove: an ideal (1,+,) of (R,+,) is…

and Prove: an ideal (1,+,) of (R,+,) is the interseetion of prime ideals only if a? E I implics a E I. [Hint: For each a E 1, there is a prime ideal (P,+, )

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter6: More On Rings

Section6.4: Maximal Ideals (optional)

Problem 23E

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19. Prove: an ideal (I,+, ) of (R, +, ) is the intersection of prime ideals if and
only if a? e I implics a E I. [Ilint: For cach a 4 I, there is a prime ideal (P, +, )

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