**Author**: Balwant Singh

**Publisher:**World Scientific

**ISBN:**9814313629

**Size**: 41.69 MB

**Format:**PDF, ePub, Docs

**Category :**Mathematics

**Languages :**en

**Pages :**390

**View:**2054

**Book Description:**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.

## An Introduction To Commutative Algebra

**Author**: Huishi Li

**Publisher:**World Scientific

**ISBN:**9789812389510

**Size**: 67.16 MB

**Format:**PDF, Kindle

**Category :**Mathematics

**Languages :**en

**Pages :**175

**View:**3819

**Book Description:**- Contains many examples and problems (with hints) - Provides a good introduction for beginners in algebraic number theory and algebraic geometry

## Basic Homological Algebra

**Author**: M. Scott Osborne

**Publisher:**Springer Science & Business Media

**ISBN:**1461212782

**Size**: 25.43 MB

**Format:**PDF, Kindle

**Category :**Mathematics

**Languages :**en

**Pages :**398

**View:**5671

**Book Description:**From the reviews: "The book is well written. We find here many examples. Each chapter is followed by exercises, and at the end of the book there are outline solutions to some of them. [...] I especially appreciated the lively style of the book; [...] one is quickly able to find necessary details." EMS Newsletter

## An Introduction To Commutative Algebra

**Author**: Huishi Li

**Publisher:**World Scientific Publishing Company

**ISBN:**9813106387

**Size**: 16.25 MB

**Format:**PDF, ePub, Mobi

**Category :**Mathematics

**Languages :**en

**Pages :**188

**View:**391

**Book Description:**Designed for a one-semester course in mathematics, this textbook presents a concise and practical introduction to commutative algebra in terms of normal (normalized) structure. It shows how the nature of commutative algebra has been used by both number theory and algebraic geometry. Many worked examples and a number of problem (with hints) can be found in the volume. It is also a convenient reference for researchers who use basic commutative algebra.

## Three Lectures On Commutative Algebra

**Author**: Holger Brenner

**Publisher:**American Mathematical Soc.

**ISBN:**0821844342

**Size**: 45.24 MB

**Format:**PDF, Docs

**Category :**Mathematics

**Languages :**en

**Pages :**190

**View:**2003

**Book Description:**This book provides careful and detailed introductions to some of the latest advances in three significant areas of rapid development in commutative algebra and its applications. The book is based on courses at the Winter School on Commutative Algebra and Applications held in Barcelona: Tight closure and vector bundles, by H. Brenner; Combinatorics and commutative algebra, by J. Herzog; and Constructive desingularization, by O. Villamayor. The exposition is aimed at graduate students who have some experience with basic commutative algebra or algebraic geometry but may also serve as an introduction to these modern approaches for mathematicians already familiar with commutative algebra. This book is published in cooperation with Real Sociedad Matematica Espanola.

## Introduction To Commutative Algebra And Algebraic Geometry

**Author**: Ernst Kunz

**Publisher:**Springer Science & Business Media

**ISBN:**1461459877

**Size**: 66.48 MB

**Format:**PDF, Docs

**Category :**Mathematics

**Languages :**en

**Pages :**238

**View:**1817

**Book Description:**Originally published in 1985, this classic textbook is an English translation of Einführung in die kommutative Algebra und algebraische Geometrie. As part of the Modern Birkhäuser Classics series, the publisher is proud to make Introduction to Commutative Algebra and Algebraic Geometry available to a wider audience. Aimed at students who have taken a basic course in algebra, the goal of the text is to present important results concerning the representation of algebraic varieties as intersections of the least possible number of hypersurfaces and—a closely related problem—with the most economical generation of ideals in Noetherian rings. Along the way, one encounters many basic concepts of commutative algebra and algebraic geometry and proves many facts which can then serve as a basic stock for a deeper study of these subjects.

## Steps In Commutative Algebra

**Author**: R. Y. Sharp

**Publisher:**Cambridge University Press

**ISBN:**9780521646239

**Size**: 58.58 MB

**Format:**PDF, ePub, Docs

**Category :**Mathematics

**Languages :**en

**Pages :**355

**View:**3604

**Book Description:**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.

## Einf Hrung In Die Kommutative Algebra Und Algebraische Geometrie

**Author**: Ernst Kunz

**Publisher:**Springer-Verlag

**ISBN:**3322855260

**Size**: 54.16 MB

**Format:**PDF, ePub, Mobi

**Category :**Mathematics

**Languages :**de

**Pages :**239

**View:**878

**Book Description:**

## Commutative Algebra

**Author**: J. William Hoffman

**Publisher:**Stylus Publishing, LLC

**ISBN:**1944534709

**Size**: 54.70 MB

**Format:**PDF, Docs

**Category :**Mathematics

**Languages :**en

**Pages :**300

**View:**413

**Book Description:**The purpose of this book is twofold: to present some basic ideas in commutative algebra and algebraic geometry and to introduce topics of current research, centered around the themes of Gröbner bases, resultants and syzygies. The presentation of the material combines definitions and proofs with an emphasis on concrete examples. The authors illustrate the use of software such as Mathematica and Singular. The design of the text in each chapter consists of two parts: the fundamentals and the applications, which make it suitable for courses of various lengths, levels, and topics based on the mathematical background of the students. The fundamentals portion of the chapter is intended to be read with minimal outside assistance, and to learn some of the most useful tools in commutative algebra. The applications of the chapter are to provide a glimpse of the advanced mathematical research where the topics and results are related to the material presented earlier. In the applications portion, the authors present a number of results from a wide range of sources without detailed proofs. The applications portion of the chapter is suitable for a reader who knows a little commutative algebra and algebraic geometry already, and serves as a guide to some interesting research topics. This book should be thought of as an introduction to more advanced texts and research topics. Its novelty is that the material presented is a unique combination of the essential methods and the current research results. The goal is to equip readers with the fundamental classical algebra and geometry tools, ignite their research interests, and initiate some potential research projects in the related areas.

## Basic Abstract Algebra

**Author**: Robert B. Ash

**Publisher:**Courier Corporation

**ISBN:**0486453561

**Size**: 28.45 MB

**Format:**PDF, Mobi

**Category :**Mathematics

**Languages :**en

**Pages :**407

**View:**5043

**Book Description:**Geared toward upper-level undergraduates and graduate students, this text surveys fundamental algebraic structures and maps between these structures. Its techniques are used in many areas of mathematics, with applications to physics, engineering, and computer science as well. Author Robert B. Ash, a Professor of Mathematics at the University of Illinois, focuses on intuitive thinking. He also conveys the intrinsic beauty of abstract algebra while keeping the proofs as brief and clear as possible. The early chapters provide students with background by investigating the basic properties of groups, rings, fields, and modules. Later chapters examine the relations between groups and sets, the fundamental theorem of Galois theory, and the results and methods of abstract algebra in terms of algebraic number theory, algebraic geometry, noncommutative algebra, and homological algebra, including categories and functors. An extensive supplement to the text delves much further into homological algebra than most introductory texts, offering applications-oriented results. Solutions to all problems appear in the text.