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Ulysse from CH
science forum beginner

Joined: 30 May 2006
Posts: 16

Posted: Tue Jun 06, 2006 8:52 am    Post subject: Re: union of prime ideals

On 14 May 2006 18:52:55 -0700, Gene13@gmail.com wrote:

 Quote: Let P_1, ... , P_n be prime ideals and let I be an ideal contained in Union of P_i. Prove that I in P_i for some i. Since no one answered, I looked into my notes. One can prove

this by induction on n and prove the induction step by separating
cases: 1) there is an index i such that I intersect P_i is contained
in the union of the other P_k's; 2) no such index exists. Does this
hint suffice ?
Gene13@gmail.com
science forum beginner

Joined: 16 Mar 2006
Posts: 32

Posted: Mon May 15, 2006 1:52 am    Post subject: union of prime ideals

Let P_1, ... , P_n be prime ideals and let I be an ideal contained in
Union of P_i.
Prove that I in P_i for some i.

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