A Primer of Commutative Algebra
by J.S. Milne
Number of pages: 75
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.
Home page url
Download or read it online for free here:
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.
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.
This wikibook is intended to give an introduction to commutative algebra; i.e. it shall comprehensively describe the most important commutative algebraic objects. The axiom of choice will be used, although there is no indication that it is true.
by Thomas J. Haines - University of Maryland
Notes for an introductory course on commutative algebra. Algebraic geometry uses commutative algebraic as its 'local machinery'. The goal of these lectures is to study commutative algebra and some topics in algebraic geometry in a parallel manner.