When you click the Amazon logo to the left of any citation and purchase the book (or other media) from Amazon.com, MIT OpenCourseWare will receive up to 10% of this purchase and any other purchases you make during that visit. This will not increase the cost of your purchase. Links provided are to the US Amazon site, but you can also support OCW through Amazon sites in other regions. Learn more.

Description

In this course students will learn about Noetherian rings and modules, Hilbert basis theorem, Cayley-Hamilton theorem, integral dependence, Noether normalization, the Nullstellensatz, localization, primary decomposition, DVRs, filtrations, length, Artin rings, Hilbert polynomials, tensor products, and dimension theory.

Prerequisites

Algebra I (18.701) and Algebra II (18.702)

Textbooks

Required

Reid, Miles. Undergraduate Commutative Algebra: London Mathematical Society Student Texts. Cambridge, UK: Cambridge University Press, April 26, 1996. ISBN: 9780521458894.

Atiyah, Michael, and Ian Macdonald. Introduction to Commutative Algebra. Reading, MA: Addison-Wesley, 1994. ISBN: 9780201407518.

Recommended

Eisenbud, David. Commutative Algebra: With a View Toward Algebraic Geometry. New York, NY: Springer-Verlag, 1999. ISBN: 9780387942698.

Grading

Grades in this class are based nearly entirely on the problem sets. In addition, each student will present (at least) one problem in class. There will be no exams.

Homework

Problem sets are due in class each Thursday of the week after they are assigned (in other words, 7 or 9 days later). On occasion, a late problem set will be accepted provided that you state (1) a good reason why you need the extra time and (2) the date when the set will be turned in. Collaboration is permitted, indeed encouraged, provided that you think through each problem on your own and write it up in your own words. Problem sets will be graded in part on the quality of the write-up.

Calendar