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Commutative Algebra by Jacob Lurie, Akhil Mathew
 
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Author
Jacob Lurie, Akhil Mathew
Publisher
Harvard University 2010
Topics: Unique factorization; Basic definitions; Rings of holomorphic functions; R-modules; Ideals; Localization; SpecR and the Zariski topology; The ideal class group;
The CRing Project: a collaborative open source textbook on commutative algebra by Shishir Agrawal, et al.
 
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Author
Shishir Agrawal, et al.
Publisher
CRing Project 2011
The CRing project is an open source textbook on commutative algebra, aiming to comprehensively cover the foundations needed for algebraic geometry at the level of EGA or SGA.
Commutative Algebra by Keerthi Madapusi
 
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Author
Keerthi Madapusi
Publisher
Harvard University 2007
Contents: Graded Rings and Modules; Flatness; Integrality: the Cohen-Seidenberg Theorems; Completions and Hensel's Lemma; Dimension Theory; Invertible Modules and Divisors; Noether Normalization and its Consequences;
A Primer of Commutative Algebra by J.S. Milne
 
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Author
J.S. Milne
Publisher
2011
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. However, they are quite concise.
A Quick Review of Commutative Algebra by Sudhir R. Ghorpade
 
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Author
Sudhir R. Ghorpade
Publisher
Indian Institute of Technology, Bombay 2000
These notes attempt to give a rapid review of the rudiments of classical commutative algebra. Some of the main results whose proofs are outlined here are: Hilbert basis theorem,
A Quick Review of Commutative Algebra by Sudhir R. Ghorpade
 
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Author
Sudhir R. Ghorpade
Publisher
Indian Institute of Technology, Bombay 2000
These notes attempt to give a rapid review of the rudiments of classical commutative algebra. Some of the main results whose proofs are outlined here are:
Introduction to Commutative Algebra by Thomas J. Haines
 
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Author
Thomas J. Haines
Publisher
University of Maryland 2005
Notes for an introductory course on commutative algebra. Algebraic geometry uses commutative algebraic as its 'local machinery'. The goal of these lecture notes is to study commutative algebra and some topics in algebraic geometry in a parallel manner.
Determinantal Rings by Winfried Bruns, Udo Vetter
 
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Author
Winfried Bruns, Udo Vetter
Publisher
Springer 1988
Determinantal rings and varieties have been a central topic of commutative algebra and algebraic geometry. 
 
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Author
Pete L. Clark
Publisher
University of Georgia 2015
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; Factorization; Dedekind domains; Picard groups.
Lectures on Commutative Algebra by Sudhir R. Ghorpade
 
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Author
Sudhir R. Ghorpade
Publisher
Indian Institute of Technology, Bombay 2006
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.
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