I would appreciate some help with developing a simple proof that the ideals in the ring of integers for a number field have the same rank as the ring of integers itself.(adsbygoogle = window.adsbygoogle || []).push({});

In other words, assuming from the start that all the ideals are finitely generated, all ideals require the same number of generators as the entire ring of integers itself.

I find it easy to show that the ideals have the same rank or lower, but not that they have to have the same rank.

Any help would be appreciated. Thanks.

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# Fintely generated ideals

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