This is a 22-lecture course, with each lecture being about 30 minutes or so, given online by Richard Borcherds. It gives an introduction to rings and modules.
- Introduction
- Group rings
- Burnside ring and rings of differential operators
- Unique factorization
- Examples of unique factorizations
- Prime and maximal ideals
- Localization
- Free modules
- Projective modules
- Tensor products of abelian groups
- Tensor products of modules
- Duality and injective modules
- Colimits and exactness
- Limits and exactness
- Polynomials
- Factorization of polynomials
- Noetherian rings
- Hilbert’s theorems
- Symmetric functions
- Resultants
- Formal power series
- Hensel’s lemma
