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Aug 1, 2010 at 17:57 comment added Hailong Dao The $a,b,c,d$ in the second sentence should perhaps be $A,B,C,D$ to avoid confusions with the third sentence. I don't want to bump the question, so this comment will suffice.
Aug 1, 2010 at 17:42 vote accept Alexander Woo
Aug 1, 2010 at 8:41 comment added Hailong Dao As I commented on damiano's answer, the reason one can not stop at $I=(a,b)$ is because the OP says "$I$ does not have codimension $n$". If we do not care about that, then there is no need for the silly-looking last 3 sentences.
Aug 1, 2010 at 4:37 history answered Hailong Dao CC BY-SA 2.5