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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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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 ? 

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