MAU34102 Commutative algebra

This module is examined in a 2-hour examination at the end of Semester 2.
Continuous assessment contributes 15% towards the overall mark.
The module is passed if the overall mark for the module is 40% or more. If the overall mark for the module is less than 40% and there is no possibility of compensation, the module will be reassessed as follows:
1) A failed exam in combination with passed continuous assessment will be reassessed by an exam in the supplemental session;
2) The combination of a failed exam and failed continuous assessment is reassessed by the supplemental exam;
3) A failed continuous assessment in combination with a passed exam will be reassessed by one or more summer assignments in advance of the supplemental session.

11 weeks of teaching with 3 lectures per week.

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.
Discrete valuation rings, Dedekind domains, p-adic numbers, Hensel's lemma.
Dimension theory.