Algebra

1 Unit · Graduate

"Category theory. Linear algebra over fields. Rings and modules: prime/maximal ideals, PIDs, structure theorem for finitely generated modules, application to the existence of Jordan form, complexes, exact sequences, snake lemma, tensor products, Hom-tensor adjointness, free resolutions. Injective and projective modules, Tor and Ext. Simple groups, solvable groups, nilpotent groups, Group actions, Sylow theorems, free groups, matrix groups."