Math 648 WINTER 2018, List of lectures
On this page I will post content of all lectures with reference to the
book. All handouts also will be posted here.
Monday, January 8: More of permutation groups. Section 7.3.
Find your homework!
Reading assignment: read pages 149-152 in the book on applications
of Burnside orbit counting Lemma.
Wednesday, January 10: PSL_n is simple. Section 7.4.
Friday, January 12: Sylow theorems. Section 7.5.
Wednesday, January 17: Applications of Sylow theory. Finite solvable groups.
Friday, January 19: Solvable groups and nilpotent groups/ Sections 8.1-8.2.
Reading assignment: look at problems on group theory in Chapter 9.
Monday, January 22: First steps in modules. Section 16.1.
Wednesday, January 24: Decomposable and indecomposable modules. Exact sequences.
Friday, January 26: Complete reducibility. Section 16.2.
Monday, January 29: Free modules. Section 16.3.
Wednesday, January 31: Chain conditions. Section 16.4.
Friday, February 2: Idempotents. Section 16.5.
Monday, February 5: Fitting Lemma and Krull-Schmidt Theorem.
New homework (due on 2/21!!!)
Wednesday, February 7: Finitely generated modules over PID. Section 17.1.
Friday, February 9: Rational canonical form for linear operators. Section 17.2.
Monday, February 12: Schur's Lemma and Jacobson density theorem.
Section 18.1. We will have MIDTERM on Friday!!!
Wednesday, February 14: Simple artinian rings (Wedderburn theorem).
Examples of semisimple rings.
Friday, February 16: Midterm. Here are the
Monday, February 19: Structure of semisimple rings: Wedderburn-Artin theorem.
Wednesday, February 21: Jacobson radical.
Sections 18.3. New homework!
Friday, February 23: More on Jacobson radical. Section 18.3.
Monday, February 26: Projective and injective modules. Section 19.1.
Wednesday, February 28: More on injective modules. Tensor product over a ring.
Sections 19.1-19.2. New homework!
Friday, March 2: More on tensor products. Sections 19.2-19.3.
Monday, March 5: Tensor product over commutative rings. Section 19.3.
Wednesday, March 7: Tensor products of algebras and external tensor products
of modules. Section 19.3. Last homework (due on Friday!)
Friday, March 9: Tensor product and Hom as adjoint functors. Section 20.1.
Monday, March 12: Additive categories. Equivalences are additive functors.
Wednesday, March 14: Properties of equivalences: exactness, projectives go to
projectiles, finite generation, generators. Sections 20.2-20.3.
Friday, March 16: Morita contexts and Morita theorems. Section 20.4.
Reading assignment: look at problems on ring theory in Chapter 21.