Ring of germs of holomorphic functions at $0\in \mathbb{C}$

Question

So I've been reading the book and they used a induction proof where they just state that for the base case the ring of germs of holomorphic functions on $\mathbb{C}$ is Noetherian. I looked at other book and they start at the trivial case $\mathbb{C}^0$, so they weren't very helpful.I was wondering why the above result is true if anyone could explain to me. Thanks.