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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.
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.
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.
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'.
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.
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.
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.
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.
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.
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.
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.
by Pete L. Clark - University of Georgia , 2011
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.
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.
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.
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.
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.