Talk:Krull's theorem
Latest comment: 11 years ago by 212.127.195.242 in topic Uniqueness?
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Proof?
editI'm going to guess that the proof of this is long and/or nontrivial - but does anyone know for sure? Is it Wikiable? Druiffic (talk) 05:10, 11 December 2008 (UTC)Druiffic
- A sketchy proof in a few lines appears in Matsumura (1987), Commutative Ring Theory. I am not that familiar with Zorn's Lemma, so I will not venture to transcribe/expand it. Wandrer2 (talk) 15:55, 7 January 2009 (UTC)
Uniqueness?
editThe article says that Krull's theorem states there is always a maximal ideal, but makes no mention of it being unique.... is it necessary that the maximal ideal be unique, or can a ring have more than one maximal ideal? — Preceding unsigned comment added by 99.149.190.128 (talk) 04:13, 12 November 2012 (UTC)
- A ring that has a unique maximal ideal is called local. Rings can have more than one maximal ideal, take the ring of integers, for every prime number p, pZ is a maximal ideal of Z. This theorem further in no way proves anything about uniqueness. 212.127.195.242 (talk) 21:43, 5 October 2013 (UTC)