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A note on minimal prime ideals. (English) Zbl 0841.13001

The aim of this very short note is to establish the following result: Let \(R\) be a commutative ring with identity, and \(I\neq R\) an ideal of \(R\). If every prime ideal minimal over \(I\) is finitely generated, then there are only finitely many prime ideals minimal over \(I\).

MSC:

13A15 Ideals and multiplicative ideal theory in commutative rings
13F99 Arithmetic rings and other special commutative rings
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References:

[1] Irving Kaplansky, Commutative rings, Revised edition, The University of Chicago Press, Chicago, Ill.-London, 1974. · Zbl 0296.13001
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