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.

What kind of result are you expecting?
– YoungsuApr 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 LandsburgApr 3 '13 at 22:18

2

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 KovácsApr 3 '13 at 22:45

Sandor: that's indeed what I meant to say. Thanks.
– Steven LandsburgApr 4 '13 at 4:16