Background Algebra for Algebraic Geometry

Warning: The slides contain many typos, beware.

It was given on the 16th of November 2024.

Chapters:
0:00 Introduction
1:08 Contents of talk
3:26 Rings and Subrings
21:44 Products and Direct Sums
26:14 Commutative Rings, Domains, and Fields
44:08 Equivalence Relations
50:35 Congruences and Quotient Rings
58:33 Ideals and their Generation
1:12:56 Principal Ideal Domains
1:28:27 Homomorphisms and Isomorphisms of Rings
1:51:15 Maximal Ideals
1:57:32 Prime Ideals
2:14:30 Modules and Algebras over a Ring
2:49:23 The Rings C(Ω)
2:54:48 Germs, Stalks, and Local Rings
3:03:14 Multiplicative Sets and Localization
3:14:05 Polynomail Rings over a Ring
3:30:26 Irreducibility and Factorization
3:37:18 Further Reading