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Commutative Algebra

e-books in Commutative Algebra category

Book cover: Commutative AlgebraCommutative 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.
(837 views)
Book cover: Frobenius Splitting in Commutative AlgebraFrobenius 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.
(1341 views)
Book cover: Theory and Applications of Lattice Point Methods for Binomial IdealsTheory 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.
(4494 views)

Book cover: Introduction to Twisted Commutative AlgebrasIntroduction 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.
(2519 views)
Book cover: The Algebraic Theory of Modular SystemsThe 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'.
(4129 views)
Book cover: Determinantal RingsDeterminantal 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.
(4895 views)
Book cover: Commutative AlgebraCommutative 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.
(4919 views)
Book cover: The CRing Project: a collaborative open source textbook on commutative algebraThe 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.
(4203 views)
Book cover: Commutative AlgebraCommutative 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.
(5121 views)
Book cover: A Primer of Commutative AlgebraA 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.
(4365 views)
Book cover: A Quick Review of Commutative AlgebraA 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.
(5108 views)
Book cover: Introduction to Commutative AlgebraIntroduction 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.
(4715 views)
Book cover: Commutative AlgebraCommutative 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.
(4686 views)
Book cover: Homological ConjecturesHomological 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.
(4212 views)
Book cover: Lectures on Commutative AlgebraLectures 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.
(3961 views)
Book cover: Trends in Commutative AlgebraTrends 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.
(6032 views)
Book cover: A Course In Commutative AlgebraA 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.
(11825 views)