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Module MAU34102: Commutative Algebra

Credit weighting (ECTS)
5 credits
Semester/term taught
Hilary Term 2019-20
Contact Hours
11 weeks, 3 lectures including tutorials per week
 Prof. Sergey Mozgovoy
Learning Outcomes
Module Content
  • Exact sequences and tensor products of modules.
  • Rings of fractions.
  • Noetherian and Artinian rings, Hilbert's basis theorem, primary decomposition.
  • Integral dependence, Noether's normalization theorem, Hilbert's Nullstellensatz.
  • Valuation theory: Discrete valuation rings, Dedekind domains, p-adic numbers, Hensel's lemma.
  • Dimension theory.
Module Prerequisite


Required Reading
  • Atiyah and Macdonald. Introduction to commutative algebra.
  • Zariski and Samuel. Commutative algebra, Vol. I and II.
  • Eisenbud. Commutative algebra.
    Assessment Detail

    This module will be examined in a 2 hour examination in Trinity term. Continuous assessment will contribute 15% to the final grade for the module at the annual examination session. Re-assessments if required will consist of 100% exam.