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.
This PDF book Progress
in Commutative Algebra 2 covers the following topics related to
Commutative Algebra : A Guide to Closure Operations in Commutative
Algebra, A Survey of Test Ideals, Finite-dimensional Vector Spaces with
Frobenius Action, Finiteness and Homological Conditions in Commutative
Group Rings, Regular Pullbacks, Noetherian Rings without Finite
Normalization, Krull Dimension of Polynomial and Power Series Rings, The
Projective Line over the Integers, On Zero Divisor Graphs, A Closer Look
at Non-unique Factorization via Atomic Decay and Strong Atoms.
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.