ementas

Commutative Algebra

Program

  1. Ideals in commutative rings.
  2. Spectrum of a ring.
  3. Zariski topology.
  4. Radicals.
  5. Modules.
  6. Tensor product.
  7. Localization.
  8. Noetherian and Artinian rings.
  9. Primary decomposition.
  10. Support.
  11. Algebraic extensions, Noether’s normalization theorem and Hilbert Nullstellensatz.
  12. Integral extensions, “going-up” and “going down” theorems.
  13. Discrete valutation rings.
  14. Invertible Ideals.
  15. Completion, Artin-Rees’ lemma, Krull’s theorem, Hensel’s theorem.
  16. Dimension theory.

Basic bibliography:

Software: CoCoA, SAGE.