Let R be a commutative ring with unity, I an arbitrary ideal in R and P1,P2,...,Pn prime ideals in R. Show that I ⊆ of the union of P_i for i=1,...,n implies that I ⊆ P_j for some j ∈ {1,2,...,n}.

Let R be a commutative ring with unity, I an arbitrary ideal in R and P1,P2,...,Pn prime ideals in R. Show that I ⊆ of the union of P_i for i=1,...,n implies that I ⊆ P_j for some j ∈ {1,2,...,n}.

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 35E: Let R be a commutative ring with unity whose only ideals are {0} and R Prove that R is a...

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Question

Let R be a commutative ring with unity, I an arbitrary ideal in R and P1,P2,...,Pn
prime ideals in R. Show that I ⊆ of the union of P_i for i=1,...,n implies that I ⊆ P_j for some j ∈ {1,2,...,n}.

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