Mathematics 423/502, Topics in Algebra
TTh 14:00-15:20, MATX 1102
Atiyah and Macdonald, Introduction to commutative algebra.
Course description :
This is a course in Commutative Algebra, with some homological algebra mixed in.
This material is of interest in its own right;
it is also important for advanced work in algebraic geometry,
algebraic topology and algebraic number theory.
Specific topic include:
Office: 1105 Math Annex
Office Hours dedicated to MATH 423/502: M 3-4, W 2-3
E-mail: reichst at math.ubc.ca
The official prerequisites are Math 412 or Math 423/501.
The most important pre-requisite not listed in the calendar
is Math 323 or equivalent.
In other words, I will expect a high comfort level with
linear algebra, and some familiarity with rings and modules.
Preliminaries on rings and ideals.
Nilradical and Jacobson radical.
- Local rings and localization.
Modules: tensor product, extension and restriction of scalars.
Noetherian and Artinian rings.
Hilbert basis theorem.
Hilbertís Nullstellensatz, Noether normalization theorem,
and an introduction to affine algebraic geometry.
Time permitting, we may explore further topics, such as
primary decomposition of ideals in Noetherian rings,
Krull dimension, valuations, or finite generation of rings of invariants.
Homework will be assigned on a bi-weekly bases.
Interaction and collaboration on homework is encouraged,
but if you collaborate, please acknowledge this in writing.
Problem Set 1. Due Tuesday, January 16.
Chapter 1, Exercises 1, 2, 4, 5, 7, 8, 10, 12.
In Exercise 5, ignore the question about the converse in (ii).
Evaluation : Course marks will be based on
the homework and two midterm exams. The midterms will be given in class
Thursday, February 15 and Thursday, March 22.