**
Math 648 WINTER 2007, List of lectures
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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: Examples of noncommutative rings. Rotman, Section 8.1.
Wednesday, January 10: Wedderburn Theorem. Rotman, Section 8.2.
Here is homework!
Friday, January 12: Modules, ideals, homomorphisms etc. Rotman, Section 8.1.
Wednesday, January 17: Jordan-Hoelder Theorem. Rotman, Section 8.2.
Friday, January 19: ACC and DCC; algebras. Rotman, Section 8.2.
New homework!
Monday, January 22: Jacobson radical. Rotman, Section 8.2.
Wednesday, January 24: Jacobson radical for artinian rings. Semisimple rings.
Rotman, Section 8.2-8.3.
Friday, January 26: Semisimple modules and rings. Rotman, Section 8.3.
New homework!
Monday, January 29: Semisimple rings and Jacobson radical. Rotman, Section 8.3.
Wednesday, January 31: Artin-Wedderburn theorem. Rotman, Section 8.3.
Friday, February 2: Group algebra is semisimple (Maschke's theorem).
Rotman, Section 8.3. New homework!
Monday, February 5: Examples of group algebra decompositions and representations.
Sections 8.3, 8.5.
Wednesday, February 7: Irreducible characters are linearly independent.
Rotman, Section 8.5.
Friday, February 9: Orthogonality relations for characters. Rotman, Section 8.5.
New homework!
Monday, February 12: Character table and second orthogonality relation. Rotman,
Section 8.5. We will have MIDTERM next Monday 1-3pm!!!
Wednesday, February 14: Tensor products of vector spaces and algebraic integers.
Rotman, Section 8.4.
Friday, February 16: Burnside theorem: group of order p^aq^b is solvable.
Rotman, Section 8.5. No new homework.
Monday, February 19: We had
Midterm today; here are the
solutions.
Wednesday, February 21: Tensor products. Rotman, Section 8.4.
Friday, February 23: More on tensor products. Rotman, Section 8.4.
New homework!
Monday, February 26: Induced representations of finite groups. Rotman, Section 8.5.
Wednesday, February 28: Formula for character of induced representation.
Frobenius reciprocity. Rotman, Section 8.5.
Friday, March 2: Frobenius groups and Frobenius theorem. Rotman, Section 8.6.
Monday, March 5: Projective modules; modules over PID. Rotman, Section 9.1.
Wednesday, March 7: Modules over PID: torsion free modules are free. Rotman, Section
9.1.
Friday, March 9: Modules over PID: primary decomposition and decomposition into
sum of cyclic modules. Rotman, Section 9.1. Last homework!
Monday, March 12: Injective modules and Baer's criterion. Examples of injective
modules. Rotman, Section 7.4.
Wednesday, March 14: Elementary divisors and invariant factors. Rotman, Section 9.1.
Friday, March 16: Rational canonical form. Rotman, Section 9.2.
THE END