Commutative Algebra

Aug-Nov 2022

Instructor:

• Manoj Kummini
  Email: mkummini AT cmi DOT ac DOT in.
  https://www.cmi.ac.in/~mkummini/index.html
  Office: GL-05

• Animesh Lahiri
  Email: animeshl AT cmi DOT ac DOT in.
  

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