Hilbert's syzygy theorem and regular local rings.
Fundamental structures for homological algebra. Sheaves: An introduction to sheaves and sheaf cohomology. K-Theory: Specifically focusing on the functors K0cap K sub 0 G0cap G sub 0 Chapter C-5: Commutative Rings III Advanced topics in commutative algebra: Advanced Modern Algebra: Third Edition, Part 2 ...
Artinian and Noetherian rings, Jacobson radicals, and Wedderburn-Artin theorems. Hilbert's syzygy theorem and regular local rings
Focuses on the theory of modules and group representations, primarily in the semisimple case: the Nielsen-Schreier theorem
Cohomology of groups, crossed products, and an introduction to spectral sequences.
Presentations, the Nielsen-Schreier theorem, and the Kurosh theorem. Chapter C-2: Representation Theory
Introduces homological algebra and its applications to groups: