This page will be updated periodically through the semester.
The assessment will comprise three assignments, due early April, mid May and late June respectively, and a peer review of the first assignment. (Peer reviews of the second and third assignments were planned, but had to be abandoned due to lack of time.) The third assignment is in the nature of a take-home examination over an extended period of time.
First Assignment due Wednesday 1 April 2009
Second Assignment due Friday 22 May 2009
Third Assignment due Friday 26 June 2009
Contents and overview of core materials
Local Rings and Residue Fields
Divisibility and Factorisation
Operations on Ideals continued
Extension and Contraction continued
Modules and Module Homomorphisms
Modules and Module Homomorphisms continued
Submodules and Quotient Modules
Operations on Submodules continued
Finitely Generated and Free Modules
Split Extensions
Snake Lemma
Introducing Tensor Products
Introducing Tensor Products continued
Multilinear Mappings and Tensor Products
Hint for last question on the second Assignment
Introducing Restriction and Extension of Scalars
Restriction and Extension of Scalars
Introducing Exactness Properties of Tensor Products
Exactness Properties of the Tensor Product
Introducing Rings of Fractions
Introducing Modules of Fractions
Connection With Tensor Products
Introducing the Fraction Functor
Modules of Fractions continued
Introducing Properties of Localisation
Some Properties of Localization
Extended and Contracted Ideals in Rings of Fractions
Extended and Contracted Ideals in Rings of Fractions continued
Introducing Primary Decompositions
Exploring Primaries, Radicals, Maximals and Powers
Background on Chain Conditions
Introducing Hilbert's Basis Theorem