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Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra
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David A Cox, PH.D.
Algebraic Geometry is the study of systems of polynomial equations in one or more variables, asking such questions as: does the system have finitely many solutions, and if so how can one find them? And if there are infinitely many solutions, how can they be described and manipulated? The solutions of a system of polynomial equations form a ...
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Commutative Algebra
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Oscar Zariski, Pierre Samuel
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Introduction to Commutative Algebra (on Demand)
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Michael Francis Atiyah
This book grew out of a course of lectures given to third year undergraduates at Oxford University and it has the modest aim of producing a rapid introduction to the subject. It is designed to be read by students who have had a first elementary course in general algebra. On the other hand, it is not intended as a substitute for the more ...
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Combinatorial Commutative Algebra
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Ezra Miller, Bernd Sturmfels
Combinatorial commutative algebra is an active area of research with thriving connections to other fields of pure and applied mathematics. This book provides a self-contained introduction to the subject, with an emphasis on combinatorial techniques for multigraded polynomial rings, semigroup algebras, and determinantal rings. The eighteen chapters ...
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Computational Methods in Commutative Algebra and Algebraic Geometry
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Wolmer Vasconcelos
From the reviews: "...Many parts of the book can be read by anyone with a basic abstract algebra course...it was one of the author's intentions to equip students who are interested in computational problems with the necessary algebraic background in pure mathematics and to encourage them to do further research in commutative algebra and algebraic ...
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Multiplicities and Chern Classes in Local Algebra
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Paul C Roberts
The theory of local Chern characters used in commutative algebra originated in topology some years ago, and from there was introduced in algebraic geometry. This book describes the theory in an algebraic setting, presenting research results and important algebraic applications, some of which come from the author's own work. It concentrates on the ...
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Joins and Intersections
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H Flenner, L O O'Carroll, W Vogel
The central topic of the book is refined Intersection Theory and its applications, the central tool of investigation being the Stuckrad-Vogel Intersection Algorithm, based on the join construction. This algorithm is used to present a general version of Bezout's Theorem, in classical and refined form. Connections with the Intersection Theory of ...
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Arithmetic of blowup algebras
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Vasconcelos
This book provides an introduction to recent developments in the theory of blow up algebras - Rees algebras, associated graded rings, Hilbert functions, and birational morphisms. The emphasis is on deriving properties of rings from their specifications in terms of generators and relations. While this limits the generality of many results, it opens ...
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A Singular Introduction to Commutative Algebra
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Gert-Martin Greuel, Gerhard Pfister, Olaf Bachmann (Contributions by)
From the reviews of the first edition: 'It is certainly no exaggeration to say that "A Singular Introduction to Commutative Algebra" aims to lead a further stage in the computational revolution in commutative algebra. Among the great strengths and most distinctive features is a new, completely unified treatment of the global and local theories, ...
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Local Cohomology: An Algebraic Introduction with Geometric Applications
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M P Brodmann, R y Sharp
This book provides a careful and detailed algebraic introduction to Grothendieck's local cohomology theory, and provides many illustrations of applications of the theory in commutative algebra and in the geometry of quasi-affine and quasi-projective varieties. Topics covered include Castelnuovo-Mumford regularity, the Fulton-Hansen connectedness ...
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Introduction to Commutative Algebra and Algebraic Geometry
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Ernst Kunz
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The Geometry of Syzygies: A Second Course in Commutative Algebra and Algebraic Geometry
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by
David Eisenbud
Algebraic Geometry often seems very abstract, but in fact it is full of concrete examples and problems. This side of the subject can be approached through the equations of a variety, and the syzygies of these equations are a necessary part of the study. This book is the first textbook-level account of basic examples and techniques in this area. It ...
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Undergraduate Commutative Algebra
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Miles Reid, C M Series (Editor), J W Bruce (Editor)
Commutative algebra is at the crossroads of algebra, number theory and algebraic geometry. This textbook is affordable and clearly illustrated, and is intended for advanced undergraduate or beginning graduate students with some previous experience of rings and fields. Alongside standard algebraic notions such as generators of modules and the ...
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Commutative Algebra
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James Thomson Knight, N J Hitchin (Editor)
This introduction to commutative algebra gives an account of some general properties of rings and modules, with their applications to number theory and geometry. It assumes only that the reader has completed an undergraduate algebra course. The fresh approach and simplicity of proof enable a large amount of material to be covered; exercises and ...
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Commutative Algebra: With a View Toward Algebraic Geometry
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J H Ewing, David Eisenbud, F W Gehring
Commutative Algebra is best understood with knowledge of the geometric ideas that have played a great role in its formation, in short, with a view towards algebraic geometry. The author presents a comprehensive view of commutative algebra, from basics, such as localization and primary decomposition, through dimension theory, differentials, ...
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Computational Commutative Algebra 1
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Martin Kreuzer, Lorenzo Robbiano
This is a book about Grobner bases and their applications. It contains 3 chapters, 20 sections, 44 tutorials, 165 exercises, and numerous further amusements. It is going to help you bridge the gap between theoretical computer algebra and actual computation. We hope you will have as much fun reading it as the authors had writing it!'This is one of ...
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The Geometry of Syzygies: A Second Course in Algebraic Geometry and Commutative Algebra
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by
David Eisenbud
Algebraic Geometry often seems very abstract, but in fact it is full of concrete examples and problems. This side of the subject can be approached through the equations of a variety, and the syzygies of these equations are a necessary part of the study. This book is the first textbook-level account of basic examples and techniques in this area. It ...
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Trends in Commutative Algebra
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by
Luchezar L Avramov (Editor), Mark Green (Editor), Craig Huneke (Editor)
In 2002, an introductory workshop was held at the Mathematical Sciences Research Institute in Berkeley to survey some of the many new directions of the commutative algebra field. Six principal speakers each gave three lectures, accompanied by a help session, describing the interaction of commutative algebra with other areas of mathematics for a ...
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Combinatorics and Commutative Algebra
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by
Richard P Stanley
Some remarkable connections between commutative algebra and combinatorics have been discovered in recent years. This book provides an overview of two of the main topics in this area. The first concerns the solutions of linear equations in nonnegative integers. Applications are given to the enumeration of integer stochastic matrices (or magic ...
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Commutative Algebra II
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Pierre Samuel, Oscar Zariski
From the Preface: 'topics are: valuation theory; theory of polynomial and power series rings (including generalizations to graded rings and modules); local algebra...the algebro-geometric connections and applications of the purely algebraic material are constantly stressed and abundantly scattered throughout the exposition. Thus, this volume can ...
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Steps in Commutative Algebra
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Sharp
This introductory account of commutative algebra is aimed at advanced undergraduates and first year graduate students. Assuming only basic abstract algebra, it provides a good foundation in commutative ring theory, from which the reader can proceed to more advanced works in commutative algebra and algebraic geometry. The style throughout is ...
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Commutative Algebras of Toeplitz Operators on the Bergman Space
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Nikolai Vasilevski
This book is devoted to the spectral theory of commutative C*-algebras of Toeplitz operators on the Bergman space and its applications. For each such commutative algebra there is a unitary operator which reduces Toeplitz operators from this algebra to certain multiplication operators, thus providing their spectral type representations. This yields ...
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Representation Theory and Algebraic Geometry
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by
A Martsinkovsky (Editor), G Todorov (Editor), J W S Cassels (Editor)
This book contains seven lectures delivered at The Maurice Auslander Memorial Conference at Brandeis University in March 1995. The variety of topics covered at the conference reflects the breadth of Maurice Auslander's contribution to mathematics, which includes commutative algebra and algebraic geometry, homological algebra and representation ...
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Commutative Algebra: Proceedings of a Microprogram Held June 15 - July 2, 1987
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by
Melvin Hochster (Editor), Craig Huneke (Editor), Judith D Sally (Editor)
The papers in this volume, some of which are expository, some strictly research, and some a combination, reflect the intent of the program. They give a cross-section of what is happening now in this area. Nearly all of the manuscripts were solicited from speakers at the conference, and in most instances the manuscript is based on the conference ...
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Introductory Course in Commutative Algebra
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Arthur Chatters, Charudatta Hajar-Navis
This text aims to offer a concise introduction to topics in commutative algebra, with an emphasis on worked examples and applications. It combines elegant algebraic theory with applications to number theory, problems in classical Greek geometry, and the theory of finite fields which has important uses in other branches of science. Topics covered ...
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