Graduate Algebra 1

UPenn MATH 6020, Fall 2024.

daniel.krashen+alg1@gmail.com

Lecture 0 (8/28/2024): Introductions and a bestiary of algebraic objects

Lecture 1 (9/9/2024): Group basics: subgroups, normality, actions, some counting

Lecture 2 (9/11/2024): The Sylow theorem and friends

Lecture 3 (9/16/2024): Group action grab-bag, group presentations

Lecture 4 (9/18/2024): Sylow experiments for order 750, products and extensions

Lecture 5 (9/23/2024): Nilpotent group, semidirect products

Lecture 6 (9/25/2024): Group extensions and their splittings

Lecture 7 (9/30/2024): Group extensions and cohomology

Lecture 8 (10/2/2024): Group cohomology

Lecture 9 (10/7/2024): The Schur-Zassenhaus Theorem

Lecture 10 (10/9/2024): Solvable and nilpotent groups

Lecture 11 (10/14/2024): Towards Jordan-Hölder

Lecture 12 (10/16/2024): The dévissage philosophy, Jordan-Hölder and start of Krull-Schmidt

Lecture 13 (10/21/2024): Review

Lecture 14 (10/28/2024): Chain conditions on X-modules

Lecture 15 (10/30/2024): Simple X-modules and complete reducibility

Lecture 16 (11/4/2024): Rings

Lecture 17 (11/6/2024): Semisimple rings

Lecture 18 (11/11/2024): Artinian rings and the Jacobson radical

Lecture 19 (11/13/2024): Wedderburn-Artin theory and introduction to categories

Lecture 20 (11/18/2024): Some category theory

Lecture 21 (11/20/2024): Exact sequences and projective modules

Lecture 22 (11/25/2024): Tensor products

Lecture 23 (12/2/2024): Bi-endomorphisms and the Morita theorems