Math 602: Commutative Algebra

WF 8:30am-9:45am in Physics 227

Office Hours: TBD

Homeworks There will be weekly homework, posted here.

Material The material covered in this course will be that of a standard commutative algebra course, but maybe not in a standard order. The material covered will roughly be (in no particular order): ideals and operations on them, varieties, localization, Noether normalization, the Nullstellansatz, Groebner bases and computations, Noetherian and Artinian conditions, radicals, primary decomposition, Hilbert polynomials, dimension theory, modules, completion, integral dependence, going up, going down, Dedekind domains and DVRS, flatness. Also, other topics as time permits.

I'll record the actual topics as we go


Textbook(s) The official textbook is Matsumura's Commutative Ring Theory. However, here are some other recommendations

Computational Component

I think it is pretty useful to actually be able to compute some things in life. So, there will be a computational component to this course. You will be able to use whatever tools you want for this --- none of the computational exercises will be programming intensive at all. They will just be enough to convince you that you can actually compute things explicitly (this is not something that you can easily see from standard treatments of commutative algebra). My favorite choices of tools are the following

Supplements

In this section I'll collect supplementary papers by others, and notes by myself.

A wonderful translation of Noether's original paper on primary decomposition.

An incomplete introduction to homological algebra via exercises: homological algebra notes