by Jacob Lurie, Akhil Mathew
Publisher: Harvard University 2010
Number of pages: 172
Topics: Unique factorization; Basic definitions; Rings of holomorphic functions; R-modules; Ideals; Localization; SpecR and the Zariski topology; The ideal class group; Dedekind domains; Hom and the tensor product; Exactness; Projective modules; Right-exactness of the tensor product; Flatness; Discrete valuation rings; The adjoint property; etc.
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by J.S. Milne
These notes prove the basic theorems in commutative algebra required for algebraic geometry and algebraic groups. They assume only a knowledge of the algebra usually taught in advanced undergraduate or first-year graduate courses.
by Ezra Miller - arXiv
This is a survey of lattice point methods for binomial ideals. It is aimed at students and researchers in algebra; it includes many examples, open problems, and elementary introductions to the motivations and background from outside of algebra.
by Sudhir R. Ghorpade - Indian Institute of Technology, Bombay
These lecture notes attempt to give a rapid review of the rudiments of classical commutative algebra. Topics covered: rings and modules, Noetherian rings, integral extensions, Dedekind domains, and primary decomposition of modules.
by Pete L. Clark - University of Georgia
Contents: 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; etc.