Abstract Algebra [Paperback]

ISBN: 9789384007249

Edition: 2nd Edition

Author : Dan Saracino

Year: 2017

Pages: 326

Publisher Name: Medtech

Rs. 295.00
Rs. 236.00

The book preserved the emphasis on providing a large number of examples and on helping students learn how to write proofs. The presentation of the sections given at a higher level. Unusual features, for a book is still relatively short, are the inclusion of full proofs of both directions of Gauss theorem on constructible regular polygons and galois theorem on solvability by radicals, a Galoistheoretic proof of the Fundamental Theorem of Algebra, and a proof the Primitive  Element Theorem.

First semester course should probably include the material of Sections 0-13, and some of the material on rings in Section 16 and the following sections, Sections 14 and 15 allow the inclusion of some deeper result on groups. In second semester it should be possible to cover the whole book, possibly omitting Section 21.

The changes include the simplification of some points in the edition of some new exercise, and the updating of some historical material. All the topics are given in step by step method with simple language to understand the concept easily. This book is intended for use in a junior-senior level course in abstract algebra. The students who used the book for the five sections as text and pointed out to me parts of the presentation that needed clarification.


  1. Sets and Induction
  2. Binary Operations
  3. Groups
  4. Fundamental Theorems about Groups
  5. Powers of a Elements; Cosets
  6. Counting the elements of a Finite Group
  7. Normal Subgroups
  8. Homomorphisms
  9. Homomorphisms and Normal Subgroups
  10. Direct Products and Finite Abelian Groups
  11. Sylow Theorems
  12. Rings
  13. Subrings, Ideals, and Quotient Rings
  14. Ring Homomorphisms
  15. Polynomials
  16. From Polynomials to Fields
  17. Unique Factorization Domains
  18. Extensions of Fields
  19. Constructions with Straightedge and Compass
  20. Normal and Separable Extensions
  21. Galois Theory
  22. Solvbability
  23. Suggestions for Further Reading
  24. Answers to Selected Exercises
  25. Index


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