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Sep 20, 2023 at 12:10 comment added Elías Guisado Villalgordo This is well-explained in Matsumura's Commutative Ring Theory (not to be confused with Commutative Algebra), section 10, until theorem 10.1 (ii).
Nov 16, 2009 at 22:45 comment added Georges Elencwajg Dear TG: you are absolutely right, and in principle I wouldn't solve an exercise from a textbook in public. I made an exception here because non-discrete valuation rings are often seen as esoteric creatures and I have never heard of a course in commutative algebra in which they are taught: I would be very happy if you decided to be an exception! Incidentally this is rather strange and might be due to Grothendieck's hatred of valuation rings, which is alleged to be one of the causes of his leaving Bourbaki. Se non è vero...
Nov 16, 2009 at 21:38 comment added TSG A minor comment: as someone who is teaching from Atiyah-Macdonald at the moment (and setting exercises from it for homework), I think there might be something to be said for not working out exercises in full "in public".
Nov 16, 2009 at 20:07 vote accept Marc Nieper-Wißkirchen
Nov 16, 2009 at 18:41 history edited Georges Elencwajg CC BY-SA 2.5
suppressed one redundant occurrence of the word "local"
Nov 16, 2009 at 14:41 history answered Georges Elencwajg CC BY-SA 2.5