book is a clear, concise, and efficient textbook, aimed at beginners, with a
good selection of topics. Topics covered includes: Rings and Ideals, Radicals,
Filtered Direct Limits, Cayley–Hamilton Theorem, Localization of Rings and
Modules, Krull–Cohen–Seidenberg Theory, Rings and Ideals, Direct Limits,
Filtered direct limit.
This note covers the following topics: introduction to commutative rings, introduction to modules, ideals, examples of
rings, Swan's theorem, localization, Noetherian rings, boolean rings, Affine
algebras and the Nullstellensatz, the spectrum, integral extensions,
factorization, dedekind domains and picard groups.