Commutative Algebra
Aug-Nov 2022
Instructor:
Lectures :
- Tue and Thu, 10:30-11:45.
- Details will be posted in the moodle course page (see
below).
Moodle:
All the information regarding this course will be posted on Moodle.
You can directly access the course page at
https://moodle.cmi.ac.in/course/view.php?id=678
. Otherwise, look for `Commutative Algebra' under
`Mathematics / Aug-Nov 2022'.
References :
- Eisenbud, Commutative Algebra with a View towards Algebraic
Geometry, Springer.
- Matsumura, Commutative Ring Theory, Cambridge.
- Reid, Undergraduate Commutative Algebra, Cambridge.
- Serre, Local Algebra, Springer.
Brief description: This is an introductory course in commutative
algebra.
- rings, ring maps, prime spectrum, maximal spectrum.
- localisation
- associated primes and primary decomposition
- integral extensions, Noether normalization lemma,
nullstellensatz
- dimension theorem for noetherian local rings, for affine
rings, principal ideal theorem.
- If time permits:
- Grobner bases, Buchberger algorithm,
elimination, ideal membership.
- completions and Hensel's lemma.
- Kahler differentials
We will use Macaulay2
extensively to study examples. Some assignments will involve
computations with Macaulay2.
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Last modified:
Mon Aug 1 21:31:36 IST 2022