Sep 5 
1.1 
Refresher on modules 
Sep 10 
1.2–1.4 
Noetherian and artinian modules and rings 
Sep 12 
1.4, 2.1 
JordanHÃ¶lder Theorem, Affine varieties, vanishing ideals 
Sep 17 
2.1–2.3 
Hilbert Basis Theorem, radical ideals 
Sep 19 
2.4 
Integral extensions 
Sep 24 
2.5 
Noether Normalization Lemma 
Sep 26 
2.6 
Hilbert's Nullstellensatz 
Oct 1 
2.7 
Localization 
Oct 3 
2.7 
Localization 
Oct 10 
3.1, 3.2 
Tensor product of modules over a commutative ring 
Oct 15 
3.3, 3.4 
Tensor product of modules over a commutative ring 
Oct 17 
3.5, 3.6 
General tensor products 
Oct 22–26 
Reading week 
Oct 29 
4.1 
Semisimple modules 
Oct 31 
4.2 
Schur's Lemma, Jacobson Density Theorem 
Nov 5 
4.3 
Semisimple rings 
Nov 7 
1.1–4.2 
Midterm test 
Nov 12 
4.4 
Properties of simple rings 
Nov 14 
4.5 
Characterization of simple rings, ArtinWedderburn Theorem 
Nov 19 
5.1, 5.2 
Categories, short exact sequences, split exact sequences 
Nov 21 
5.3 
Exact functors 
Nov 26 
5.4 
Projective modules 
Nov 28 
5.5 
Injective modules 
Dec 3 
5.6, 5.7 
Embedding into an injective module, flat modules 
Dec 5 

Further directions. Discussion of final exam 