e-books in Commutative Algebra category
Progress in Commutative Algebra 2: Closures, Finiteness and Factorizationby 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...
(4261 views)
Commutative Algebra and Noncommutative Algebraic Geometryby 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.
(6090 views)
Frobenius Splitting in Commutative Algebraby 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.
(7069 views)
Theory and Applications of Lattice Point Methods for Binomial Idealsby 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.
(9065 views)
Introduction to Twisted Commutative Algebrasby 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.
(7380 views)
The Algebraic Theory of Modular Systemsby 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'.
(9689 views)
Determinantal Ringsby 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.
(11254 views)
Commutative Algebraby 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.
(11145 views)
The CRing Project: a collaborative open source textbook on commutative algebraby 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.
(9862 views)
Commutative Algebraby 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.
(11361 views)
A Primer of Commutative Algebraby 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.
(9652 views)
A Quick Review of Commutative Algebraby 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.
(10403 views)
Introduction to Commutative Algebraby Thomas J. Haines - University of Maryland , 2024
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.
(10163 views)
Commutative Algebraby 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.
(11664 views)
Homological Conjecturesby 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.
(10847 views)
Lectures on Commutative Algebraby 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.
(9375 views)
Trends in Commutative Algebraby 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.
(10952 views)
A Course In Commutative Algebraby 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.
(17564 views)