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If R is a local Noetherian regular ring and I is an ideal contained in the maximal ideal. Can we compare the number of minimal set of generator of I and I^2? Thanks a lot for helping me.

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What kind of result are you expecting? –  Youngsu Apr 3 '13 at 20:57
    
Let $I$ be generated by $n$ elements. Then clearly $I^2$ requires at most $n^2$ generators, and clearly this bound is realized for the local ring of the origin in affine $n$-space. So what more might you hope to say? –  Steven Landsburg Apr 3 '13 at 22:18
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Steven, in a commutative ring you can get away with $n+1 \choose 2$ generators for $I^2$. This works for your example as well. –  Sándor Kovács Apr 3 '13 at 22:45
    
Sandor: that's indeed what I meant to say. Thanks. –  Steven Landsburg Apr 4 '13 at 4:16
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