The CRing Project: a collaborative open source textbook on commutative algebra
by Shishir Agrawal, et al.
Publisher: CRing Project 2011
Number of pages: 493
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. It is a work in progress. The present project aims at producing a work suitable for a beginning undergraduate with a background in elementary abstract algebra.
Download or read it online for free here:
by Keerthi Madapusi - Harvard University
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; Quasi-finite Algebras; etc.
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 Steven V Sam, Andrew Snowden - arXiv
An expository account of the theory of twisted commutative algebras, which can be thought of as a theory for handling commutative algebras with large groups of linear symmetries. Examples include the coordinate rings of determinantal varieties, 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.