 # Commutative Algebra

## e-books in Commutative Algebra category Progress in Commutative Algebra 2: Closures, Finiteness and Factorization
by - 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...
(729 views) Commutative Algebra and Noncommutative Algebraic Geometry
by - Cambridge University Press ,
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.
(2038 views) Commutative Algebra
- Wikibooks ,
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.
(2815 views) Frobenius Splitting in Commutative Algebra
by - arXiv ,
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.
(3045 views) Theory and Applications of Lattice Point Methods for Binomial Ideals
by - arXiv ,
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.
(6035 views) Introduction to Twisted Commutative Algebras
by - 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.
(3895 views) The Algebraic Theory of Modular Systems
by - Cambridge University Press ,
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'.
(6042 views) Determinantal Rings
by - 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.
(6909 views) Commutative Algebra
by - 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.
(6763 views) The CRing Project: a collaborative open source textbook on commutative algebra
by - 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.
(6005 views) Commutative Algebra
by - 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.
(7006 views) A Primer of Commutative Algebra
by ,
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.
(6170 views) A Quick Review of Commutative Algebra
by - Indian Institute of Technology, Bombay ,
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.
(6851 views) Introduction to Commutative Algebra
by - 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.
(6489 views) Commutative Algebra
by - University of Georgia ,
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.
(6570 views) Homological Conjectures
by - University of Nebraska - Lincoln ,
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.
(7587 views) Lectures on Commutative Algebra
by - 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.
(5630 views) Trends in Commutative Algebra
by - 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.
(7514 views) A Course In Commutative Algebra
by - University of Illinois ,
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.
(13659 views)