I.2.11

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.