Are "Commutative Algebra" and "Algebraic Geometry" useful for physics? Hello, I'm considering taking Commutative Algebra, and perhaps even Algebraic Geometry (for which the previous is a prerequisite). In the first place I would take it for the enjoyment of mathematics and to give me an all-round mathematical education (even though I'm not into abstract algebra, leaning more toward analysis-type stuff, think differential geometry etc). But I was wondering, is there also a value in, say, commutative algebra from a physicist point of view? (I suppose if one goes deep enough in string theory, one can find it being used somewhere but I hope you understand I'm (in the first place, at least) looking for a less terribly-specific application.) Thank you.