Commutative Algebra: An Introduction by William HoffmanCommutative Algebra: An Introduction by William Hoffman

Commutative Algebra: An Introduction

byWilliam Hoffman, Xiaohong Jia, Haohao Wang

Hardcover | May 13, 2016

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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 asMathematicaandSingular.

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. Thefundamentalsportion of the chapter is intended to be read with minimal outside assistance, and to learn some of the most useful tools in commutative algebra. Theapplicationsof 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.
William Hoffman is a professor of Mathematics at Louisiana State University.Xiaohong Jia is a professor at Chinese Academy of Sciences.Haohao Wang is a professor of Mathematics at Southeast Missouri State University.
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Title:Commutative Algebra: An IntroductionFormat:HardcoverDimensions:300 pages, 9.41 × 7.24 × 0.98 inPublished:May 13, 2016Publisher:Mercury Learning & InformationLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:1944534601

ISBN - 13:9781944534608

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Table of Contents

1. Introduction
2. Rings and Ideals
3. Modules
4. Graded and Local Rings and Modules
5. Homological Method
Bibliography
Index