The Algebraic Theory of Modular Systems
by Francis Sowerby Macaulay
Publisher: Cambridge University Press 1916
Number of pages: 140
Many of the ideas introduced by F.S. Macaulay in this classic book have developed into central concepts in what has become the branch of mathematics known as Commutative Algebra. Today his name is remembered through the term 'Cohen-Macaulay ring'.
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by Jacob Lurie, Akhil Mathew - Harvard University
Topics: Unique factorization; Basic definitions; Rings of holomorphic functions; R-modules; Ideals; Localization; SpecR and Zariski topology; The ideal class group; Dedekind domains; Hom and the tensor product; Exactness; Projective modules; etc.
by Shishir Agrawal, et al. - CRing Project
The CRing project is an open source textbook on commutative algebra, aiming to comprehensively cover the foundations needed for algebraic geometry at the EGA or SGA level. Suitable for a beginning undergraduate with a background in abstract algebra.
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 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.