19. Prove: an ideal (I, +, ) of (R,+, ·) is the intersection of prime ideals if andonly if a? E I implies a E 1. [Ilint: For each a 4 1, there is a prime ideal (P,+, )of (R,+, ) which is maximal with respect to disjointedness from the set{a, a², . .. , a",...

Let I,+,· is an ideal of R,+,·. To prove that I is the intersection of prime ideals if and only if…

Answered: 19. Prove: an ideal (I, +, ·) of (R,+,…

19. Prove: an ideal (I, +, ·) of (R,+, ·) is the intersection of prime ideals if and only if a? E I implies a E I. [llint: For cach a 4 1, there is a prime ideal (P,+,)

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

19. Prove: an ideal (I, +, ) of (R,+, ·) is the intersection of prime ideals if and
only if a? E I implies a E 1. [Ilint: For each a 4 1, there is a prime ideal (P,+, )
of (R,+, ) which is maximal with respect to disjointedness from the set
{a, a², . .. , a",
...

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