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It would seem more logical to start with the residue field of a (local) ring! Unless, of course, you believe that schemes come before commutative rings. Arcfrk 20:12, 24 April 2007 (UTC)
Oh, I do think rings come before schemes. I didn't know that one speaks of residue fields of local rings, too. I only knew the scheme-context of this notion. So, please go ahead and enhance the description. Jakob.scholbach 22:37, 24 April 2007 (UTC)