Term 2 2016
Commutative Algebra is the study of commutative rings, their modules
and ideals. This theory has developed over the last 150 years not just
as an area of algebra considered for its own sake, but as a tool in
the study of two enormously important branches of mathematics:
algebraic geometry and algebraic number theory.
See also the description in the
| Diane Maclagan
||C2.26 Zeeman Building
|| D.Maclagan at warwick.ac.uk
||(024) 7652 8333
Course Times and Location
|| MS.01 (Zeeman building)
|| Monday 16:00-17:00
|| H0.51 (Humanities)
|| Wednesday 10:00 -11:00
|| MS.02 (Zeeman building)
|| Thursday 12:00 -13:00
| Support class
|| B1.01 (Zeeman building)
|| Thursday 13:00-14:00
Much of this module will follow Reid's Undergraduate
commutative algebra. An excellent reference for the material on
Grübner bases is Ideals, Varieties, and Algorithms, by
Cox, Little, O'Shea.
A comprehensive introduction to commutative algebra is
Eisenbud's Commutative algebra with a view toward algebraic
geometry. I will follow the notation and conventions of this book
(though we will only cover a fraction of it in ten weeks!) A classic
reference is Atiyah, MacDonald Introduction to commutative
Other references include Sharp's Steps in commutative
algebra, and Zariski and Samuel's Commutative
algebra. There are multiple copies of these books in the library; the links above are to the catalogue.
If you want to buy copies of any of these books, I
recommend first looking at a site
Alibris.co.uk, which searches multiple independent bookstores.
There is a forum
for this module. You are strongly encouraged to ask any questions you
have about the module on this forum (as well as in/after class, in
support class, and in office hours). You can also answer other
people's questions if you know the answer. Any emails about this
module without personal content will be answered on the forum, and
such questions asked on the forum will always take priority over
A handout introducing Macaulay 2 is available here.
A handout for the lectures on primary decomposition is available here.
There will be homework assignments every two weeks. Homework
assignments and due dates will be posted on the
schedule webpage, which will also have
the reading for the following week. You are encouraged to work on
homework together, but you should write up the solutions yourself.
No late homework will be accepted. The lowest homework score will be
dropped, however, when calculating your homework mark. Homework will
be due at 2pm on the Tuesdays indicated on the schedule page (except
week 10, which is due on Thursday).
Your final mark for this module will depend 15% on your homework,
and 85% on the examination in Term 3.