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 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.
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 Christopher Francisco, et al. - De Gruyter Open
This volume contains surveys on closure operations, finiteness conditions and factorization. Closure operations on ideals and modules are a bridge between noetherian and nonnoetherian commutative algebra. It contains a guide to closure operations...
by Luchezar L. Avramov, at al. - Cambridge University Press
This book focuses on the interaction of commutative algebra with other areas of mathematics, including algebraic geometry, group cohomology and representation theory, and combinatorics, with all necessary background provided.