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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 Zorns 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

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