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Commutative Algebra Chapters 1 7

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Commutative Algebra

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Commutative Algebra by N. Bourbaki Book Summary:

This is the softcover reprint of the English translation of 1972 (available from Springer since 1989) of the first 7 chapters of Bourbaki's 'Algèbre commutative'. It provides a very complete treatment of commutative algebra, enabling the reader to go further and study algebraic or arithmetic geometry. The first 3 chapters treat in succession the concepts of flatness, localization and completions (in the general setting of graduations and filtrations). Chapter 4 studies associated prime ideals and the primary decomposition. Chapter 5 deals with integers, integral closures and finitely generated algebras over a field (including the Nullstellensatz). Chapter 6 studies valuation (of any rank), and the last chapter focuses on divisors (Krull, Dedekind, or factorial domains) with a final section on modules over integrally closed Noetherian domains, not usually found in textbooks. Useful exercises appear at the ends of the chapters.

Commutative Algebra

Commutative Algebra Chapters 1 7 [Pdf/ePub] eBook

Commutative Algebra by N. Bourbaki Book Summary:

This is the softcover reprint of the English translation of 1972 (available from Springer since 1989) of the first 7 chapters of Bourbaki's 'Algèbre commutative'. It provides a very complete treatment of commutative algebra, enabling the reader to go further and study algebraic or arithmetic geometry. The first 3 chapters treat in succession the concepts of flatness, localization and completions (in the general setting of graduations and filtrations). Chapter 4 studies associated prime ideals and the primary decomposition. Chapter 5 deals with integers, integral closures and finitely generated algebras over a field (including the Nullstellensatz). Chapter 6 studies valuation (of any rank), and the last chapter focuses on divisors (Krull, Dedekind, or factorial domains) with a final section on modules over integrally closed Noetherian domains, not usually found in textbooks. Useful exercises appear at the ends of the chapters.

Elements of Mathematics

Commutative Algebra Chapters 1 7 [Pdf/ePub] eBook

Elements of Mathematics by Nicolas Bourbaki Book Summary:

Download or read Elements of Mathematics book by clicking button below to visit the book download website. There are multiple format available for you to choose (Pdf, ePub, Doc).

Algebra I

Commutative Algebra Chapters 1 7 [Pdf/ePub] eBook

Algebra I by N. Bourbaki Book Summary:

This softcover reprint of the 1974 English translation of the first three chapters of Bourbaki’s Algebre gives a thorough exposition of the fundamentals of general, linear, and multilinear algebra. The first chapter introduces the basic objects, such as groups and rings. The second chapter studies the properties of modules and linear maps, and the third chapter discusses algebras, especially tensor algebras.

Algèbre commutative

Commutative Algebra Chapters 1 7 [Pdf/ePub] eBook

Algèbre commutative by N. Bourbaki Book Summary:

Ce volume du Livre d’Algèbre commutative, septième Livre du traité, comprend les chapitres: 8. Dimension ; 9. Anneaux locaux noethériens complets. Le chapitre 8 traite de diverses notions de dimension en algèbre commutative, telles que la dimension de Krull d’un anneau. Ces notions jouent un rôle capital en géometrie algébrique. Le chapitre 9 introduit, quant à lui, les vecteurs de Witt et les anneaux japonais.

Lie Groups and Lie Algebras

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Lie Groups and Lie Algebras by Nicolas Bourbaki Book Summary:

Download or read Lie Groups and Lie Algebras book by clicking button below to visit the book download website. There are multiple format available for you to choose (Pdf, ePub, Doc).

Elements of Mathematics

Commutative Algebra Chapters 1 7 [Pdf/ePub] eBook

Elements of Mathematics by Nicolas Bourbaki Book Summary:

Download or read Elements of Mathematics book by clicking button below to visit the book download website. There are multiple format available for you to choose (Pdf, ePub, Doc).

Commutative Algebra: Constructive Methods

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Commutative Algebra: Constructive Methods by Henri Lombardi,Claude Quitté Book Summary:

Translated from the popular French edition, this book offers a detailed introduction to various basic concepts, methods, principles, and results of commutative algebra. It takes a constructive viewpoint in commutative algebra and studies algorithmic approaches alongside several abstract classical theories. Indeed, it revisits these traditional topics with a new and simplifying manner, making the subject both accessible and innovative. The algorithmic aspects of such naturally abstract topics as Galois theory, Dedekind rings, Prüfer rings, finitely generated projective modules, dimension theory of commutative rings, and others in the current treatise, are all analysed in the spirit of the great developers of constructive algebra in the nineteenth century. This updated and revised edition contains over 350 well-arranged exercises, together with their helpful hints for solution. A basic knowledge of linear algebra, group theory, elementary number theory as well as the fundamentals of ring and module theory is required. Commutative Algebra: Constructive Methods will be useful for graduate students, and also researchers, instructors and theoretical computer scientists.

Commutative Algebra

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Commutative Algebra by Marco Fontana,Sophie Frisch,Sarah Glaz Book Summary:

This volume presents a multi-dimensional collection of articles highlighting recent developments in commutative algebra. It also includes an extensive bibliography and lists a substantial number of open problems that point to future directions of research in the represented subfields. The contributions cover areas in commutative algebra that have flourished in the last few decades and are not yet well represented in book form. Highlighted topics and research methods include Noetherian and non- Noetherian ring theory as well as integer-valued polynomials and functions. Specific topics include: · Homological dimensions of Prüfer-like rings · Quasi complete rings · Total graphs of rings · Properties of prime ideals over various rings · Bases for integer-valued polynomials · Boolean subrings · The portable property of domains · Probabilistic topics in Intn(D) · Closure operations in Zariski-Riemann spaces of valuation domains · Stability of domains · Non-Noetherian grade · Homotopy in integer-valued polynomials · Localizations of global properties of rings · Topics in integral closure · Monoids and submonoids of domains The book includes twenty articles written by many of the most prominent researchers in the field. Most contributions are authored by attendees of the conference in commutative algebra held at the Graz University of Technology in December 2012. There is also a small collection of invited articles authored by those who did not attend the conference. Following the model of the Graz conference, the volume contains a number of comprehensive survey articles along with related research articles featuring recent results that have not yet been published elsewhere.

Commutative Algebra

Commutative Algebra Chapters 1 7 [Pdf/ePub] eBook

Commutative Algebra by David Eisenbud Book Summary:

This is a comprehensive review of commutative algebra, from localization and primary decomposition through dimension theory, homological methods, free resolutions and duality, emphasizing the origins of the ideas and their connections with other parts of mathematics. The book gives a concise treatment of Grobner basis theory and the constructive methods in commutative algebra and algebraic geometry that flow from it. Many exercises included.

Basic Commutative Algebra

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Basic Commutative Algebra by Balwant Singh Book Summary:

This textbook, set for a one or two semester course in commutative algebra, provides an introduction to commutative algebra at the postgraduate and research levels. The main prerequisites are familiarity with groups, rings and fields. Proofs are self-contained. The book will be useful to beginners and experienced researchers alike. The material is so arranged that the beginner can learn through self-study or by attending a course. For the experienced researcher, the book may serve to present new perspectives on some well-known results, or as a reference.

Fuzzy Commutative Algebra

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Fuzzy Commutative Algebra by John N Mordeson,D S Malik Book Summary:

This book is the first to be devoted entirely to fuzzy abstract algebra. It presents an up-to-date version of fuzzy commutative algebra, and focuses on the connection between L-subgroups of a group, and L-subfields of a field. In particular, an up-to-date treatment of nonlinear systems of fuzzy intersection equations is given. Contents:L-Subsets and L-SubgroupsL-Subgroups of Abelian GroupsL-Subrings and L-IdealsL-SubmodulesL-SubfieldsStructure of L-Subrings and L-IdealsAlgebraic L-Varieties and Intersection EquationsL-SubspacesGalois Theory and Group L-Subalgebras Readership: Pure mathematicians. Keywords:Fuzzy Subsets;Fuzzy Subgroups;Fuzzy Subrings;Fuzzy Ideals;Fuzzy Submodules ;Fuzzy Subfields;Fuzzy Varieties;Fuzzy Subspaces;Fuzzy Galois Theory;Fuzzy Group SubalgebrasReviews: “The book is self-contained … This will serve as a nice reference book for researchers in the field. It may also be used as a good text for an advanced graduate course. There are a good number of exercises at the end of each chapter of the book.” Mathematical Reviews

Undergraduate Commutative Algebra

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Undergraduate Commutative Algebra by Reid Miles,Miles Reid Book Summary:

In this well-written introduction to commutative algebra, the author shows the link between commutative ring theory and algebraic geometry. In addition to standard material, the book contrasts the methods and ideology of modern abstract algebra with concrete applications in algebraic geometry and number theory. Professor Reid begins with a discussion of modules and Noetherian rings before moving on to finite extensions and the Noether normalization. Sections on the nullstellensatz and rings of fractions precede sections on primary decomposition and normal integral domains. This book is ideal for anyone seeking a primer on commutative algebra.

Algebra II

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Algebra II by N. Bourbaki Book Summary:

This is a softcover reprint of chapters four through seven of the 1990 English translation of the revised and expanded version of Bourbaki’s Algebre. Much material was added or revised for this edition, which thoroughly establishes the theories of commutative fields and modules over a principal ideal domain.

Rational Points and Arithmetic of Fundamental Groups

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Rational Points and Arithmetic of Fundamental Groups by Jakob Stix Book Summary:

The section conjecture in anabelian geometry, announced by Grothendieck in 1983, is concerned with a description of the set of rational points of a hyperbolic algebraic curve over a number field in terms of the arithmetic of its fundamental group. While the conjecture is still open today in 2012, its study has revealed interesting arithmetic for curves and opened connections, for example, to the question whether the Brauer-Manin obstruction is the only one against rational points on curves. This monograph begins by laying the foundations for the space of sections of the fundamental group extension of an algebraic variety. Then, arithmetic assumptions on the base field are imposed and the local-to-global approach is studied in detail. The monograph concludes by discussing analogues of the section conjecture created by varying the base field or the type of variety, or by using a characteristic quotient or its birational analogue in lieu of the fundamental group extension.

Steps in Commutative Algebra

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Steps in Commutative Algebra by R. Y. Sharp Book Summary:

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 rigorous but concrete, with exercises and examples given within chapters, and hints provided for the more challenging problems used in the subsequent development. After reminders about basic material on commutative rings, ideals and modules are extensively discussed, with applications including to canonical forms for square matrices. The core of the book discusses the fundamental theory of commutative Noetherian rings. Affine algebras over fields, dimension theory and regular local rings are also treated, and for this second edition two further chapters, on regular sequences and Cohen–Macaulay rings, have been added. This book is ideal as a route into commutative algebra.

Lie Groups and Lie Algebras

Commutative Algebra Chapters 1 7 [Pdf/ePub] eBook

Lie Groups and Lie Algebras by N. Bourbaki Book Summary:

From the reviews of the French edition: "This is a rich and useful volume. The material it treats has relevance well beyond the theory of Lie groups and algebras, ranging from the geometry of regular polytopes and paving problems to current work on finite simple groups having a (B,N)-pair structure, or ‘Tits systems’". --G.B. Seligman in MathReviews.

Topologie générale

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Topologie générale by N. Bourbaki Book Summary:

Ce deuxième volume du Livre de Topologie générale décrit de nombreux outils fondamentaux en topologie et en analyse, tels que le théorème d’Urysohn, le théorème de Baire ou les espaces polonais. Il comprend les chapitres : 1. Groupes à un paramètre ; 2. Espaces numériques et espaces projectifs ; 3. Les groupes additifs Rn ; 4. Nombres complexes ; 5. Utilisation des nombres réels en topologie générale ; 6. Espaces fonctionnels.

Manuscripta Mathematica

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Manuscripta Mathematica by N.A Book Summary:

Download or read Manuscripta Mathematica book by clicking button below to visit the book download website. There are multiple format available for you to choose (Pdf, ePub, Doc).