Bibliographic Information

Basic abstract algebra

P.B. Bhattacharya, S.K. Jain, S.R. Nagpaul

Cambridge University Press, c1994

2nd ed

  • : pbk

Available at  / 23 libraries

Search this Book/Journal

Note

Includes bibliographical references (p. 476) and index

Description and Table of Contents

Description

This book represents a complete course in abstract algebra, providing instructors with flexibility in the selection of topics to be taught in individual classes. All the topics presented are discussed in a direct and detailed manner. Throughout the text, complete proofs have been given for all theorems without glossing over significant details or leaving important theorems as exercises. The book contains many examples fully worked out and a variety of problems for practice and challenge. Solutions to the odd-numbered problems are provided at the end of the book. This new edition contains an introduction to lattices, a new chapter on tensor products and a discussion of the new (1993) approach to the celebrated Lasker-Noether theorem. In addition, there are over 100 new problems and examples, particularly aimed at relating abstract concepts to concrete situations.

Table of Contents

  • Preface to the second edition
  • Preface to the first edition
  • Glossary of symbols
  • Part I. Preliminaries: 1. Sets and mappings
  • 2. Integers, real numbers, and complex numbers
  • 3. Matrices and determinants
  • Part II. Groups: 4. Groups
  • 5. Normal subgroups
  • 6. Normal series
  • 7. Permutation groups
  • 8. Structure theorems of groups
  • Part III. Rings and Modules: 9. Rings
  • 10. Ideals and homomorphisms
  • 11. Unique factorization domains and euclidean domains
  • 12. Rings of fractions
  • 13. Integers
  • 14. Modules and vector spaces
  • Part IV. Field Theory: 15. Algebraic extensions of fields
  • 16. Normal and separable extensions
  • 17. Galois theory
  • 18. Applications of Galios theory to classical problems
  • Part V. Additional Topics: 19. Noetherian and Artinian modules and rings
  • 20. Smith normal form over a PID and rank
  • 21. Finitely generated modules over a PID
  • 22. Tensor products
  • Solutions to odd-numbered problems
  • Selected bibliography
  • Index.

by "Nielsen BookData"

Details

  • NCID
    BA2430172X
  • ISBN
    • 0521460816
    • 0521466296
  • LCCN
    93037548
  • Country Code
    uk
  • Title Language Code
    eng
  • Text Language Code
    eng
  • Place of Publication
    Cambridge ; New York
  • Pages/Volumes
    xx, 487 p.
  • Size
    24 cm
  • Classification
  • Subject Headings
Page Top