Integrated MSc-PhD Program


KSM4E15: Commutative Algebra


Topics covered include 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 Nullstellensätze, dimension theory of Noetherian local rings, and the Krull principal ideal theorem.

Suggested texts:

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