Math 800, Commutative Algebra, Fall 2013

This course is a first graduate course in commutative algebra. We will discuss modules, affine algebras, localization, transcendence degree, chain conditions, Krull dimension, and applications to other parts of mathematics as time permits. We will cover a substantial portion of the text with the notable exception that we will not discuss Galois theory (which is covered by math 740).

This course is meant to fulfill the role of math 817 in providing a graduate level abstract algebra course, while also covering different and useful material for those who have taken 817 in its previous noncommutative incarnation. In particular it is meant to be accessible to new graduate students who have done undergrad abstract algebra as well as appropriate for students who have taken 817

Lectures are Wednesday and Friday 2:30-4:20. The room will be AQ5007 until the K9509 renovations are complete, after which we will be in K9509.

Announcements

The due date for the written project has been moved to Monday December 9.
Some cohomology notes by Peter Webb. The initial motivating section is not from a particularly algebraic perspective, but the rest is.
Please let me know what project topic you have chosen by November 1. More information about the project.

Assignments

Assignment 1, due Friday September 27 in class. Solutions.
Assignment 2, due Friday October 18 in class. Solutions.
Assignment 3, due Friday November 8 in class. Solutions.
Assignment 4, due Friday November 29 in class. Solutions.

Class Notes

If you find mistakes, larger or small, please download the tex, fix them and then email me the tex and pdf back. Mahdieh has put a comment at the end of her tex file indicating the version; let's use that to keep track of revisions.

September 6 (tex). Scribe: Mahdieh
September 11 (tex). Scribe: Brad
September 13 (tex). Scribe: Nav
September 18 (tex). Scribe: Yue
September 20 (tex). Scribe: Gleb
September 25 (tex). Scribe: Brett
September 27 (tex). Scribe: Stefan
October 2: no class
October 4 (tex). Scribe Mahdieh
October 9 (tex). Scribe Brad
October 11 (tex). Scribe Nav
October 16 (tex). Scribe Steve
October 18 (tex). Scribe Gleb
October 23 (tex). Scribe Stefan
October 25 (tex). Scribe Yue
October 30 (tex). Scribe Brett
November 1 (tex). Scribe Nav
November 6 (tex). Scribe Mahdieh
November 8 (tex). Scribe Gleb
November 13 (tex). Scribe Brett
November 15 (tex). Scribe Stefan
November 20. Lecture cancelled
November 22 (tex). Scribe Brad
November 27. presentations: Brad, Brett, and Stefan.
November 29. presentations: Nav, Mahdieh, and Gleb.

Projects

Introduction to Kähler differentials by Navid Alaei.
Completion and related constructions by Brett Nasserden.
The Function Field Analogue of Dirichlet’s Theorem on Primes in Arithmetic Progressions by Gleb Glebov.
Combinatorial Nullstellensatz by Brad R. Jones.
Coefficients Of The Hilbert Polynomial Of A Determinental Ideal by Stefan Trandafir
Semilattice Polymorphisms and Chordal Graphs by Mahdieh Malekian.

Information

Syllabus

Instructor:: Karen Yeats
Office:: SS K 10508
Email:: karen_yeats at sfu.ca
Office Hours:: TBA
Lectures:: 2:30-4:20 WF, AQ5007 until K9509 is ready, K9509 once it is ready.
Textbook:: "Graduate Algebra: Commutative View" by Louis Rowen, Graduate Studies in Mathematics, 73, 2006. ISBN-13: 978-0-8218-0570-1