Unformatted text preview: a , b ∈ RQ . Then a / ∈ P j and b / ∈ P k for some j , k ∈ J . Since { P j } is a chain, without loss of generality we may assume that P j ⊆ P k . Then a , b / ∈ P j and since P j is a prime ideal, we deduce that ab / ∈ P j and hence ab / ∈ Q . Therefore Q ∈ A and is an upper bound for the chain. We conclude by Zorn’s Lemma that A has maximal elements. This means that R has minimal prime ideals with respect to inclusion....
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 Fall '07
 PALinnell
 Math, Algebra, Order theory, Prime number, pj, maximal ideal, prime ideals, prime ideal

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