# I.2.11

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This problem depends on I.2.6 so has H = 2, V = 4; (I.2.6> I.1.10> I.1.6).

### Commutative Algebra

• Say $(R,m)$ is Noeth, local then $\dim R \le \#$ of gen. for $m$

### HAPPY

• part a) is the statement that $V(f_1, ... , f_n) = V(f_1)\cap ... \cap V(f_n)$
• for part b) localize at $I(Y)$ and use the commutative algebra result.
• for part c follow the hint.