## e-books in Commutative Algebra category

**Progress in Commutative Algebra 2: Closures, Finiteness and Factorization**

by

**Christopher Francisco, et al.**-

**De Gruyter Open**,

**2012**

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...

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**3280**views)

**Commutative Algebra and Noncommutative Algebraic Geometry**

by

**David Eisenbud, et al.**-

**Cambridge University Press**,

**2015**

The books cover birational geometry, D-modules, invariant theory, matrix factorizations, noncommutative resolutions, singularity categories, support varieties, tilting theory, etc. These volumes reflect the lively interaction between the subjects.

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**5063**views)

**Frobenius Splitting in Commutative Algebra**

by

**Karen E. Smith, Wenliang Zhang**-

**arXiv**,

**2014**

Frobenius splitting has inspired a vast arsenal of techniques in commutative algebra, algebraic geometry, and representation theory. The purpose of these lectures is to give a gentle introduction to Frobenius splitting for beginners.

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**6127**views)

**Theory and Applications of Lattice Point Methods for Binomial Ideals**

by

**Ezra Miller**-

**arXiv**,

**2010**

This is a survey of lattice point methods for binomial ideals. It is aimed at students and researchers in algebra; it includes many examples, open problems, and elementary introductions to the motivations and background from outside of algebra.

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**8273**views)

**Introduction to Twisted Commutative Algebras**

by

**Steven V Sam, Andrew Snowden**-

**arXiv**,

**2012**

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.

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**6575**views)

**The Algebraic Theory of Modular Systems**

by

**Francis Sowerby Macaulay**-

**Cambridge University Press**,

**1916**

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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**8791**views)

**Determinantal Rings**

by

**Winfried Bruns, Udo Vetter**-

**Springer**,

**1988**

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.

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**10181**views)

**Commutative Algebra**

by

**Jacob Lurie, Akhil Mathew**-

**Harvard University**,

**2010**

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.

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**9919**views)

**The CRing Project: a collaborative open source textbook on commutative algebra**

by

**Shishir Agrawal, et al.**-

**CRing Project**,

**2011**

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.

(

**8997**views)

**Commutative Algebra**

by

**Keerthi Madapusi**-

**Harvard University**,

**2007**

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.

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**10276**views)

**A Primer of Commutative Algebra**

by

**J.S. Milne**,

**2011**

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.

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**8837**views)

**A Quick Review of Commutative Algebra**

by

**Sudhir R. Ghorpade**-

**Indian Institute of Technology, Bombay**,

**2000**

These notes give a rapid review of the rudiments of classical commutative algebra. Some of the main results whose proofs are outlined here are: Hilbert basis theorem, primary decomposition of ideals in noetherian rings, Krull intersection theorem.

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**9523**views)

**Introduction to Commutative Algebra**

by

**Thomas J. Haines**-

**University of Maryland**,

**2005**

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.

(

**9242**views)

**Commutative Algebra**

by

**Pete L. Clark**-

**University of Georgia**,

**2015**

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.

(

**10618**views)

**Homological Conjectures**

by

**Tom Marley, Laura Lynch**-

**University of Nebraska - Lincoln**,

**2010**

This course is an overview of Homological Conjectures, in particular, the Zero Divisor Conjecture, the Rigidity Conjecture, the Intersection Conjectures, Bass' Conjecture, the Superheight Conjecture, the Direct Summand Conjecture, etc.

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**10094**views)

**Lectures on Commutative Algebra**

by

**Sudhir R. Ghorpade**-

**Indian Institute of Technology, Bombay**,

**2006**

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.

(

**8396**views)

**Trends in Commutative Algebra**

by

**Luchezar L. Avramov, at al.**-

**Cambridge University Press**,

**2005**

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.

(

**10038**views)

**A Course In Commutative Algebra**

by

**Robert B. Ash**-

**University of Illinois**,

**2006**

This is a text for a basic course in commutative algebra, it should be accessible to those who have studied algebra at the beginning graduate level. The book should help the student reach an advanced level as quickly and efficiently as possible.

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**16499**views)