TITLE: Commutative/noncommutative algebra?
QUESTION [8 upvotes]: I know basic knowledge of undergraduate algebra till galois theory of finite extensions. I want to learn number theory, but also like algebra. This semester I have to choose to read either commutative algebra or noncommutative algebra. Can somebody tell me briefly the nature of both and what they lead? i want to know what they deal with and also in what way they are relevant in number theory. Thanks!

REPLY [5 votes]: I'll also point out that commutative algebra is at least half the foundation of modern algebraic geometry. The objects of algebraic geometry are built by sticking together a collection of geometric structures associated to a commutative ring-so to study them, one must know plenty of commutative algebra. And if you're interested in going very far into number theory, you'll likely want to learn some algebraic geometry eventually.