Integrated MSc-PhD Program

SYLLABUS

KSM3E04: Commutative Algebra

Rings and modules, morphisms, Prime spectrum of a ring, tensor products and change of base rings, Localization, Noetherian and Artinian rings, associated primes and primary decomposition, integral extensions, Noether normalization and Nullstellensatz, dimension theory of Noetherian local rings, Krull principal ideal theorem.

Suggested texts:

1. 1. 1. 1. 1. 1. Introduction to Commutative Algebra – Atiyah M. F. and McDonald I. G.
               2. Commutative Algebra – Matsumura
               3. Commutative Algebra with a View Toward Algebraic Geometry – Eisenbud, David