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, a?, ..., a", ...}

Let R be ring and Let I be an ideal of R.

Answered: and Prove: an deal (7, F,') of (R, -+,)…

and Prove: an deal (7, F,') of (R, -+,) is the intersection of prime ideals only if a2 E I implies a E I. [I/int: 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, a?, ..., a", ...}

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