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Basic Abstract Algebra

Basic Abstract Algebra

2nd Edition

textbook
  • Date Published: March 1995
  • availability: Available
  • format: Paperback
  • isbn: 9780521466295

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  • 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.

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    Product details

    • Edition: 2nd Edition
    • Date Published: March 1995
    • format: Paperback
    • isbn: 9780521466295
    • length: 508 pages
    • dimensions: 235 x 154 x 26 mm
    • weight: 0.74kg
    • availability: Available
  • 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.

  • Authors

    P. B. Bhattacharya

    S. K. Jain

    S. R. Nagpaul

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