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 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.
by Winfried Bruns, Udo Vetter - Springer
Determinantal rings and varieties have been a central topic of commutative algebra and algebraic geometry. The book gives a coherent treatment of the structure of determinantal rings. The approach is via the theory of algebras with straightening law.
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.