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Mar 21, 2010 at 22:03 comment added Emerton Dear 7-adic, it is not just a question of loving reduced schemes. See my answer below for an elaboration.
Mar 21, 2010 at 18:53 vote accept 7-adic
Mar 21, 2010 at 18:53
Mar 21, 2010 at 18:51 comment added 7-adic Thanks for your answer. I guess that the following fact makes the $I\cap J$ better: $R/I\cap J$ is reduced if both $R/I$ and $R/J$ are reduced. We 'love' reduced scheme more than non-reduced scheme.
Mar 21, 2010 at 15:44 history answered Georges Elencwajg CC BY-SA 2.5