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 

Localization 
Oct 3 

Localization 
Oct 10 

Tensor product of modules over a commutative ring 
Oct 15 

Tensor product of modules over a commutative ring 
Oct 17 

General tensor products 
Oct 22–26 
Reading week 
Oct 29 

Semisimple modules, examples, equivalent characterizations of semisimple modules, submodules and quotients of semisimple modules 
Oct 31 

Schur's Lemma, Jacobson Density Theorem 
Nov 5 

Definition of semisimple rings, decomposition of a semisimple ring into its basic building blocks 
Nov 7 

Midterm test 
Nov 12 

Decomposition of a semisimple ring into its basic building blocks, properties of simple rings 
Nov 14 

Characterization of simple rings, ArtinWedderburn Theorem 
Nov 19 

Short exact sequences, split short exact sequences 
Nov 21 

Left exactness of Hom, right exactness of the tensor product 
Nov 26 

Projective modules 
Nov 28 

Injective modules 
Dec 3 

Flat modules 
Dec 5 

Review 