| 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 |
Jordan-Hölder 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, Artin-Wedderburn 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 |