Advanced Algebra

Along with a companion volume Basic Algebra

  • Anthony W. Knapp

Part of the Cornerstones book series (COR)

Table of contents

  1. Front Matter
    Pages i-xxiv
  2. Anthony W. Knapp
    Pages 1-75
  3. Anthony W. Knapp
    Pages 76-122
  4. Anthony W. Knapp
    Pages 123-165
  5. Anthony W. Knapp
    Pages 166-261
  6. Anthony W. Knapp
    Pages 262-312
  7. Anthony W. Knapp
    Pages 313-402
  8. Anthony W. Knapp
    Pages 403-446
  9. Anthony W. Knapp
    Pages 447-519
  10. Anthony W. Knapp
    Pages 520-557
  11. Anthony W. Knapp
    Pages 558-648
  12. Back Matter
    Pages 649-730

About this book

Introduction

Basic Algebra and Advanced Algebra systematically develop concepts and tools in algebra that are vital to every mathematician, whether pure or applied, aspiring or established. Together, the two books give the reader a global view of algebra and its role in mathematics as a whole.

Key topics and features of Advanced Algebra:

*Topics build upon the linear algebra, group theory, factorization of ideals, structure of fields, Galois theory, and elementary theory of modules as developed in Basic Algebra

*Chapters treat various topics in commutative and noncommutative algebra, providing introductions to the theory of associative algebras, homological algebra, algebraic number theory, and algebraic geometry

*Sections in two chapters relate the theory to the subject of Gröbner bases, the foundation for handling systems of polynomial equations in computer applications

*Text emphasizes connections between algebra and other branches of mathematics, particularly topology and complex analysis

*Book carries on two prominent themes recurring in Basic Algebra: the analogy between integers and polynomials in one variable over a field, and the relationship between number theory and geometry

*Many examples and hundreds of problems are included, along with hints or complete solutions for most of the problems

*The exposition proceeds from the particular to the general, often providing examples well before a theory that incorporates them; it includes blocks of problems that illuminate aspects of the text and introduce additional topics

Advanced Algebra presents its subject matter in a forward-looking way that takes into account the historical development of the subject. It is suitable as a text for the more advanced parts of a two-semester first-year graduate sequence in algebra. It requires of the reader only a familiarity with the topics developed in Basic Algebra.

Keywords

Algebra Group theory Homological algebra algebraic geometry algebraic number theory finite field number theory ring theory

Authors and affiliations

  • Anthony W. Knapp
    • 1
  1. 1.East SetauketUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-8176-4613-4
  • Copyright Information Birkhäuser Boston 2008
  • Publisher Name Birkhäuser, Boston, MA
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-8176-4522-9
  • Online ISBN 978-0-8176-4613-4
  • Series Print ISSN 2197-182X
  • Series Online ISSN 2197-1838
  • About this book