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Algebra

A Teaching and Source Book

  • Ernest Shult
  • David Surowski

Table of contents

  1. Front Matter
    Pages i-xxii
  2. Ernest Shult, David Surowski
    Pages 1-19
  3. Ernest Shult, David Surowski
    Pages 21-71
  4. Ernest Shult, David Surowski
    Pages 73-103
  5. Ernest Shult, David Surowski
    Pages 105-136
  6. Ernest Shult, David Surowski
    Pages 137-161
  7. Ernest Shult, David Surowski
    Pages 163-184
  8. Ernest Shult, David Surowski
    Pages 185-230
  9. Ernest Shult, David Surowski
    Pages 231-277
  10. Ernest Shult, David Surowski
    Pages 279-332
  11. Ernest Shult, David Surowski
    Pages 333-354
  12. Ernest Shult, David Surowski
    Pages 355-441
  13. Ernest Shult, David Surowski
    Pages 443-469
  14. Ernest Shult, David Surowski
    Pages 471-527
  15. Back Matter
    Pages 529-539

About this book

Introduction

This book presents a graduate-level course on modern algebra. It can be used as a teaching book – owing to the copious exercises – and as a source book for those who wish to use the major theorems of algebra.

The course begins with the basic combinatorial principles of algebra: posets, chain conditions, Galois connections, and dependence theories. Here, the general Jordan–Holder Theorem becomes a theorem on interval measures of certain lower semilattices. This is followed by basic courses on groups, rings and modules; the arithmetic of integral domains; fields; the categorical point of view; and tensor products.

Beginning with introductory concepts and examples, each chapter proceeds gradually towards its more complex theorems. Proofs progress step-by-step from first principles. Many interesting results reside in the exercises, for example, the proof that ideals in a Dedekind domain are generated by at most two elements. The emphasis throughout is on real understanding as opposed to memorizing a catechism and so some chapters offer curiosity-driven appendices for the self-motivated student.

Keywords

Fields Groups Rings Jordan-Hölder Theorem Modern Algebra Modular Lattices Posets Wedderburn's Theorem

Authors and affiliations

  • Ernest Shult
    • 1
  • David Surowski
    • 2
  1. 1.Department of MathematicsKansas State UniversityManhattanUSA
  2. 2.(deceased)ManhattanUSA

Bibliographic information